Supporting Information Modha and Singh SI Text The Largest Previous Network. The largest previous network of the

macaque brain consists of 95 vertices and 2,402 edges [1], where the network models brain regions as vertices and the presence of long distance connections as directed edges between them. This network is displayed in Figure S1 and should be compared to our network in Figure 1 of the main text. It can be seen that the largest previous network completely misses corticosubcortical and subcortico-subcortical long distance connections and has significant gaps even amongst corticocortical long distance connections. Two-thirds of our data has never even been previously compiled, let alone analyzed and understood. CoCoMac Database. We briefly summarize the CoCoMac database,

and refer the reader to the original publications for more details [2, 3, 4, 5, 6]. CoCoMac consists of three primary databases: literature, mapping, and connectivity. • Each included literature study is assigned a unique identifier,

LitID. For example, the paper by Pandya and Seltzer in 1982 [7] is referred to as PS82. • A BrainMap is a parcellation or mapping scheme used in a particular study. A BrainMap is also referred to using LitID. A particular study may define and use a new BrainMap or it may use a previously defined map by another study. Thus, there are fewer BrainMaps than LitIDs. A BrainMap is a set of BrainRegions, where a brain region refers to cortical and subcortical subdivisions (area, region, nucleus, etc.) as well as to combinations of such subdivisions into sulci, gyri, and other large ensembles1 . A brain region is uniquely identified as a concatenation of the BrainMap that it belongs to and its Acronym, that is, as LitID-Acronym. For example, V1 in FV91 [8] is uniquely referred to as FV91-V1 whereas V1 in RD96 [9] is uniquely referred to as RD96-V1. Further, various BrainRegions are related to each other via six logical mapping relations, namely, identity (I), sub-structure (S), supra-structure (L), and overlapping structure (O), expanded lamina (E), and collapsed lamina (C). • Connectivity database consists of a set of records representing directed long distance connections from a source BrainRegion to a target BrainRegion. Further, each connection is annotated by experimentally determined strength: 1 for weak/sparse, 2 for moderate, 3 for strong/heavy, X for unspecified density, and 0 for absence of tested projection. Statistics of Downloaded Databases. When downloading the

database, we have ignored the fields PDC, Ref.text, and Ref.fig. We now enumerate gross statistics of the downloaded database. • • • • •

410 unique LitIDs (literature studies) 379 unique BrainMaps (parcellation schemes) 6,877 unique BrainRegions 1,880 unique Acronyms 10,681 unique, directed connections from one BrainRegion to another with density labels “1”, “2”, “3”, or “X” • 13,498 unique records showing tested but not found connections between a pair of BrainRegions with density label “0” • 16,712 unique records interrelating BrainRegions to each other: 9,134 I relations, 3,185 L relations, 3,185 S relations, 662 O relations, 272 E relations, and 272 C relations. The downloaded database had a number of errors that had to be corrected, for example, incorrect associations between acronyms and brain regions, lack of acronym field in the connectivity database, the supra-structure relation L not being the symmetric transpose of substructure relation S, the relations I and O not being the symmetric 1

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transpose of themselves, brain regions with different acronyms but with the same full name, typographical errors, incorrect case, missing special characters, existence of brain regions without mapping or connectivity relations, incorrect L and I relations, self-loops in L relation, missing relations, and so on. Constructing a Network and a Hierarchical Brain Map. Let us rep-

resent mapping relations I, L, O, E, C and the connectivity relation CNZ as two-dimensional binary matrices. The rows as well as columns correspond to various brain regions. The (i, j)-th entry of I relation is 1 if there exists an identity relation between the brain regions corresponding to row i and column j, and zero otherwise. Similarly, for L, O, E, C matrices the (i, j)-th entry is 1 if there exists the associated relation between the brain regions corresponding to row i and column j. For CNZ matrix, 1 denotes the presence of a connection between brain regions of corresponding row and column. From a matrix-theoretic view point, merging a pair of brain regions i and j amounts to, for each of the six matrices, computing a logical OR of their respective rows and columns, updating the respective rows and columns by the ORed value, and removing one each of the rows and columns, thus reducing the numbers of rows and columns by one. At any time, only a binary (zero or non-zero) entry is maintained for each of the matrices. We now give a brief description of our data processing pipeline, a series of manual and algorithmic data transformations that transform initial matrices of size 6,877 × 6,877, into compact final matrices of size 383 × 383. At the end, I, E, and C become identity matrices, L becomes the adjacency matrix of our hierarchical brain map, and the final CNZ has 6,602 non-zero entries – the edges of our network. In the initial matrices, the connectivity information is scattered across brain regions, literature studies, and parcellation schemes. This information has to be pieced together because: 1. Different studies performed at different times by different groups by using different techniques on different animals and at different resolutions, inevitably lead to a wide variety of nomenclature and parcellation schemes. For example, connectivity information for primary visual area is scattered across 42 different reports that study V1, 15 different reports that study brain region 17, and 6 different reports that study StriateC. 2. Without aggregating connectivity information of equivalent brain regions, one would only see disconnected path fragments. This point is illustrated in Figure S2 that shows how establishing equivalences between identical brain regions and then merging them is essential to uncovering reciprocal connections or to uncover a short circular loop. 3. Merging of equivalent brain regions is essential for network analysis. For example, the shortest path between two regions captures the degree of coupling between them. The longest shortest path in the network captures the extremum over all pairs, and is known as the diameter. Without merging, the brain’s connectivity appears significantly sparser than it actually is, for example, the diameter appears dramatically larger, namely, 13, than it actually is, namely, 6. Consequently, in order to obtain a complete and correct picture of the brain’s connectivity, it is imperative that brain regions that are identical are merged into a single region. We now formalize the key difficulty in merging. Define conflict relation as the intersection, logical conjunction, of I and L. In other words, conflict happens when two regions are identified both via the 1

CoCoMac refers to BrainRegion as BrainSite.

Modha & Singh

identity and superstructure relations. For example, the database contains statements: FEF and 8A are identical and that FEF is a superstructure of 8A. The relations I and L are transitive [4]. So, if A is identical to B, and B is identical to C, then A is implied to be identical to C. The space of all implied identity and superstructure relations are captured by their respective transitive closures I+ and L+ . In matrix-theoretic parlance: I+ = I ∨ I2 ∨ . . ., where ∨ represents OR or logical disjunction. It should be noted that I+ and L+ contain a combinatorial large number of entries. We now extend the definition of conflict relation to mean the intersection between I+ and L+ . Conflicts arising because of transitivity are far too numerous, are inherently insidious, and are extremely difficult to track and to eliminate (see Figure S3). We highlight an interesting sub-routine inspired by ORT[3, Appendix E] that we have repeatedly used for merging. The idea is to computes a submatrix J of I such that intersection of J+ and L+ is empty. Then, J is a conflict-free identity relation, and can be safely used for merging. This is pictorially described in Figure S4 2 . Our goal is to derive a CNZ for network analysis, with emphasis being on merging equivalent brain regions. Towards that our relation J has a number of desirable properties. Specifically, even after merging with J, each brain region can be uniquely identified with one and only one of the merged brain regions. If two original brain regions had a L relationship before merging, then the relationship is preserved amongst the merged regions. Further, J is such that no two equivalence classes of brain regions can be further merged without creating a conflict. Our algorithm greedily computes such a J and stops when conflicts are detected. On detection we can either use the computed J to merge the set of brain regions, or examine the conflict3 . In certain cases, the conflict is resolved manually using the slice-based atlas of the Rhesus monkey cortex [10]. This lends a physical constraint to the logical processing described above. Throughout the merging process, we ensure that two brain regions within a literature study are never merged unless they are explicitly identified as equivalent. This ensures that every parcellation originally present in CoCoMac is represented in our data. It is desirable to organize merged brain regions into a coherent, unified hierarchical brain map. A hierarchical brain map provides a natural frame of reference to place, understand, and correlate various brain regions. For network analysis, a hierarchical brain map provides a tool to vary the resolution of network, to analyze aggregate connectivity patterns. For example, without a hierarchical brain map, we can observe that V4 connects to TF, but cannot answer how many total connections are made between occipital lobe and temporal lobe. The key difficulty in defining a unified hierarchical brain map is that underlying L relation is a directed acyclic graph (not a tree) and contains multiple disjoint components. The key steps that we have taken to overcome this are: 1. Removed redundancy and simplified L. Specifically, if A is a superstructure of B, then all superstructure relations from A to any descendants of B are removed. This is done repeatedly through the pipeline4 . 2. Used a number of existing brain maps from CoCoMac, underlying literature, and existing atlases, for example, GM (a brain map based on conceptual relationships), R00 (a topographical regional map), and the slice-based atlas of the Rhesus monkey cortex [10, 11]. As pre-processing, we merged all laminae into their respective brain regions (using relations E and C), merged all brain regions with the same Acronym, and removed all cycles from L ensuring that it is a directed acyclic graph. As main processing steps, we merged the equivalent brain regions and placed them in a coherent parcellation. As post-processing, we merged pairs of (non-equivalent) brain regions such that one is a child of another if (a) the child is a leaf in the overall parcellation and the child does not have two-way connectivity (that is both to- and from-) or if (b) the parent region has no other 2

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children. In both of these cases, the resolution is not useful for connectivity studies, and is sacrificed for the sake of conciseness, and the regions are merged. Further, from the view point of connectivity analysis, the resulting parcellation has the pleasing property that every leaf brain region has two-way connectivity. Throughout, we preserved every single connectivity datum with care except that we removed all direct self-loops and all indirect self-loops in the form of connections between a brain region and its ascendants or descendants (where ascendants and descendants are defined with respect to the above hierarchical brain map). For overlap relation O, note that there are 9,134 I relations and 3,185 L relations, but only 662 O relations in CoCoMac. The symmetry implies that there actually only 331 O relations. The impact of overlap is mitigated due to the following reasons, 1. Thinking of I, L, O as binary set relations, overlap is a weaker relationship than subset which in turn is weaker than identity. As a result, 112 O relations are subsumed by I and 26 relations are subsumed by L. 2. Even if there is overlap between brain regions in mapping relation, there is often no overlap in connectivity which further mitigates any effect of overlaps. This subsumes 50 more O relations. Net, only 143 O relations are present in our final data. Two arbitrary brain regions have, on an average, 96% distinct connections, while brain regions involved in the 143 overlap relations have, on an average, 79% distinct connections. Thus, even if there is overlap in mapping and connectivity, the overlapping regions have substantially different connectivity and whether they can be merged is debatable. We visualize the 143 O relations in Figure S5. Despite ignoring the O relationship, we find that most remaining O relationships lie close to the diagonal for a depth first order scan of our brain map. Consequently, overlap is mostly between siblings or cousin vertices in the hierarchy, or between regions like 25 and 14 that are known to be adjacent on the cortex. In summary, merging equivalent brain region is imperative for network-analysis. It is interesting to note that 93% of the original I relations are respected in our hierarchical brain map, that is the corresponding brain regions are merged. The hierarchy that we obtain is at the highest resolution that the data can meaningfully support. Given a set of merged regions, the hierarchy is invaluable for visualization (Figure S6 and the derivative figures) and for aggregate connectivity analysis (Tables S2 and S3), but does not play a role in networkanalysis. The final set of merged regions and the hierarchical brain map are visualized in Figure S6 and described in Table S1 for complete transparency. Hierarchical Brain Map. The final resulting parcellation has 383

unique, hierarchically organized, merged brain regions. The entire set of merged brain regions and the complete parcellation are explicitly detailed in the multi-page Table S1 to provide transparency and to permit future additions as data with finer resolution becomes available. We explain the table: 1. The first column shows “Level” of a node with respect to this parcellation, where, the root node “Br” (brain) has level 0, its immediate children (DiE, Cx, BG, MB#2, OFC) have level 1, and their immediate children have level 2, and so on. 2. For each set of merged brain regions, one of the merged regions was chosen manually to represent the entire set. The second column shows the Acronym corresponding to the chosen representative brain region which is used to label the entire set. To ensure 2

J can be considered to be a valid path in the transform graph of ORT[3, Figure 5, Appendix E]. We make the simplifying assumption of not using O relation, see discussion below. 3 In contrast ORT uses PDC, manually inserted labels coding the precision of descriptions, to find the optimal valid path in the transformation graph. 4 A, B represents sets of merged brain regions

Modha & Singh

3.

4.

5. 6. 7.

consistent nomenclature, we have simply carried the Acronyms over from CoCoMac. It is important to note that there is a one-toone correspondence between a vertex in the network and a representative brain region. The third column shows the full name of the representative brain region that has also been carried over from CoCoMac. Within square brackets, the third column also shows the Acronyms of the brain regions that have been merged into the representative brain region. For example, 17, 17 I, LVQ, OC, StriateC, StriateC-I, StriateC-II, StriateC-III, StriateC-IV, UVQ, V1 I, V1 II, V1 III, have all been merged in V1. To avoid unnecessary clutter, if a brain region is merged, but had no connectivity information associated with it, then it is not shown within the square brackets. The hierarchical brain map is displayed in Figure S6. The figure contains one center and 11 concentric rings. The center is assigned the number 0, the innermost ring is assigned the number 1, and outer rings are assigned a progressively larger number. Each brain region resides on one of these rings, and the fourth column of the table displays the corresponding ring number for each brain region. The fifth column shows the total number of edges that the vertex (corresponding to the brain region) touches in the long distance network shown in Figure 1 of the main text. The sixth column shows how often the set of merged brain regions have been have been studied in the literature reports compiled by CoCoMac. The seventh column shows the number of unique connections (with density labels “1”, “2”, “3”, and “X”) reported for the set of merged brain regions in the literature reports compiled by CoCoMac.

Dataset. The dataset consists of three text files:

1. Macaque LongDistance Network.nameslist: 2 column text file. The first column is a numerical index and second column is the Acronym string of the corresponding brain region. The Acronym of brain regions are listed in the second column of Table S1. There are 383 rows corresponding to the 383 brain regions in our network. The brain regions are ordered identically in the data file and in Table S1. 2. Macaque LongDistance Network connectivity.edgelist: 2 column text file. Each row corresponds to a directed edge in the network between a source brain region and a target brain region. The first column is the index of the source brain region and the second column is the index of the target brain region, where the indices are from Macaque LongDistance Network.nameslist. There are 6602 rows corresponding to the nonzero entries in CNZ. 3. Macaque LongDistance Network mapping.edgelist: 2 column text file. Each row corresponds to a parent-child relationship in our hierarchical brain map. The first column is the index of the parent brain region and the second column is the index of the child brain region, where the indices are from Macaque LongDistance Network.nameslist. There are 382 rows corresponding to the nonzero entries in L. Visualizing the Hierarchical Brain Map: Efficient use of Space. Our

brain map is a large, unbalanced hierarchy, and effectively visualizing it within the confines of a two-dimensional page is a tremendous challenge. We explored how to effectively use space to make the hierarchy understandable and accessible to a wide audience. Radial tree is often used to layout hierarchies [12]. In this layout a single vertex, namely, the root of the hierarchy is placed at the center of the display, and all the other vertices are arranged on concentric rings around it. The center is assigned the number 0, the innermost ring is assigned the number 1, and outer rings are assigned a progressively larger number. In a conventional radial tree layout, each vertex lies on the ring corresponding to its shortest distance from the root 3

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along the hierarchy, that is, the shortest number of hops required to travel from the vertex to the root. Note that this distance corresponds exactly to the first column in Table S1. On one hand, conventional radial tree layout naturally captures the hierarchy. On the other hand, for large hierarchies, the leaf vertices tend to overlap rendering the labels unreadable [13]. Conventional tree layout algorithm starts with the root at the center and works radially outwards according to the inherent hierarchy. We now describe a novel, alternate radial tree layout algorithm that starts with the leaves at a common periphery and works radially inwards. 1. Compute shortest path from every vertex to the root. 2. From these shortest paths, determine the length of the longest shortest path, say, L. Note that L = 9 for our hierarchy. 3. Traverse the hierarchy in a breadth-first fashion. As the leaf vertices are encountered by this traversal, assign to them ring numbers in a round-robin manner: L, L + 1, . . ., L + k, L, L + 1, . . ., L + k, and so on. Note that in our experiments, we found that k = 2 leads to sufficient spacing between the leaf vertices. 4. Recursively, for every non-leaf vertex, assign to it the ring number that is one less than the minimum ring number assigned to its children. This ring numbering algorithm will naturally assign the number zero to the root. Once again, the root of the hierarchy, is placed at the center of the display, and all the other vertices are arranged on concentric rings around it. Each vertex lies on the ring corresponding to its ring number. When applied to our hierarchy, this algorithm leads to Figure S6. A disadvantage of Figure S6 is that the ring numbers do not correspond to the hierarchical levels. We compensate for this by listing both the ring numbers and the hierarchical levels in Table S1. On the advantages, it can be seen that the leaf vertices do not occlude one another and peripheral space is efficiently used. This maximizes the amount of white space in the center which we utilize to effectively display the brain network in Figure 1 of the main text. Visualizing the Hierarchical Brain Map: Effective use of Color.

“It is not the form that dictates the color, but the color that brings out the form.” Hans Hofmann The symmetry and circularity of alternate radial tree layout naturally evokes an analogy with the color wheel. We color the vertices of the hierarchical brain map based on the HSV color wheel [14]. For even better discrimination amongst the leaf vertices, we rotate the color wheel by 120 degrees for the second outermost ring, and by 240 degrees for the outermost ring. Further, we have used black text color throughout for labeling individual vertices. Figure S6 as well as all our figures, unless noted otherwise, use this default coloring template. As can be seen, color vibrantly affects presentation [15]. Accessibility is an important criteria for drawing large hierarchies such as ours. Given the small font size that the limited page size imposes, the accessibility is a particular concern in regards to the text labels used to annotate each vertex in the hierarchy. Black text in our default coloring template is harder to discern on darker background, especially, dark blue. We provide two alternate methods to enhance accessibility. 1. For higher-resolution, easier-to-read access to the hierarchy, we zoom into various sub-structures of Figure S6 in Figures S7, S8, S9, S10, S11, S12, S13, and S14. 2. For improving the contrast between foreground text labels and background color, we provide an alternative to Figure S6. Specifically, we use white foreground with dark background, and black foreground with light background in Figure S15. Visualization of the Long Distance Network. Using the brain regions

in the hierarchical brain map as vertices, we extract a network containing 6,602 edges wherein an edge encodes the presence of long Modha & Singh

distance connection between corresponding brain regions. Drawing each edge as a straight line between the two terminal vertices leads to a highly cluttered visualization where no details are discernible, as shown in Figure S17(a). Consequently, for clarity, an innovative approach is needed to reduce cluster while still preserving as much information as possible. One of the ways to reduce clutter is to bundle similar edges somehow. We employ the award-winning hierarchical edge bundling algorithm proposed by Danny Holten [16]: “Hierarchical edge bundling is based on the principle of visually bundling adjacency edges together analogous to the way electrical wires and network cables are merged into bundles along their joint paths and fanned out again at the end, in order to make an otherwise tangled web of wires and cables more manageable.” Suppose that we are trying to render an edge in the long distance network from a source vertex to a destination vertex. To this end, our hierarchical brain map can be used as a natural scaffold as in [16]. 1. Compute the path along the hierarchy from each of these two vertices to the central root vertex (Br). 2. Define the lowest common ancestor as that vertex at which these paths first meet. 3. Define a hierarchical path between two vertices as a path from the source vertex to the lowest common ancestor vertex, and from the lowest common ancestor vertex to the destination vertex. 4. Render a spline curve using this hierarchical path as the control polygon. The spline curve is then used to visualize the edge between the two vertices, instead of the direct line connecting the two vertices. 5. The spline rendering algorithm uses a bundling factor β, 0 ≤ β ≤ 1, that controls how close the spline curve is to the control polygon. Higher β implies more closeness and, consequently, more bundling between splines having common control polygon points. The bundling process and the effect of the bundling factor β are illustrated via an example in Figure S16 and via the whole network in Figure S17. It can be seen that as bundling factor increases, clutter decreases, and structure emerges. Having constructed and visualized our network, we now proceed to analyze it. Classical Fiber Systems. The visual system [8], the dorsal-ventral pathways [17], thalamocortical relays [18], and numerous corticocortical, corticosubcortical, and subcortico-subcortical fiber systems [19] serve as the very basis of our understanding of white matter pathways in the brain. Table S4 enumerates brain regions involved in these fiber systems. Comprehensiveness of our network is underscored by the fact that it contains logical sub-networks corresponding to all these physical fiber systems as demonstrated in Figures S18, S19, S20, and S21. Strongly Connected Component. For our network, only 4.5% of the

possible connections exist, so the network is sparse. A large fraction of connections, namely, 42%, are reciprocal. Out of 383 regions, 351 regions have both efferent and afferent connectivity and these form a strongly connected component (SCC) such that each such region is reachable from every other. Six regions have only efferent connections to the SCC, three regions have only afferent connections from the SCC, and the remaining 23 regions have no connections and consist of big container regions, for example, cortex (Cx), diencephalon (DiE), basal ganglia (BG), etc., that are required to hold the hierarchy together. The SCC contains 6,491 connections (roughly 98.32%), and its surprisingly large size implies that the brain invests tremendous communication resources in talking to and listening to itself. Within the SCC, the average in- and out-degrees are both 18.81. 4

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Six Degrees of Separation. The shortest path between two regions

captures the degree of coupling between them. The longest shortest path in the network captures the extremum over all pairs, and is known as the diameter. For the SCC, quite surprisingly, the diameter is actually 6, exactly! Thus, the brain has the proverbial six degrees of separation [20], and the “gossip” about every brain region’s activity spreads to every other region within the SCC in six hops or less. Diameter of corticocortical network is even smaller, namely, just 5. Small World Networks. The average shortest path between any two

pairs of vertices is known as the characteristic path length (L). The average fraction of allowable edges between neighbors of any region that actually exist is known as the average clustering coefficient (C). Random networks are characterized by small values of L and C, while regular networks are characterized by large values of L and C. For the SCC, we have that L = 2.62 which is small compared to a regular network and that C = 0.33 which is high compared to a random network (C = 0.0528, 100 trials). The brain is neither completely random nor completely regular. Rather, these values of L and C imply that even our comprehensive and colossal long distance brain network is small-world [21, 22]. Dynamically smallworld networks are characterized by “enhanced signal-propagation speed, computation power, and synchronizability” [21] all properties clearly manifested in the brain. What separates the brain network from a random network is its inherent clustering and complexity [23, 24]. Complex System. By using hierarchical relation between brain re-

gions, it is now possible for us to study not just individual connections between pairs of brain regions, but rather aggregate connections between any two larger sub-structures as well. Such aggregation can be performed at many different levels of hierarchy representing different resolutions, for example, temporal lobe may studied at a finer granularity or various cortical constituents can all be combined to permit a coarser perspective. This permits a deeper analysis and understanding of how different structures and sub-structures connect and interact with each other, see, for example, Table S2 for a summary view of corticocortical and corticosubcortical systems. It can be seen Cx is heavily connected with itself, whereas DiE and BG are heavily connected with Cx. Further refining Table S2, in Table S3, we summarize the number of connections in major corticocortical and corticosubcortical pathways by dividing Cx into its six constituents: TL#2, FL#2, Pl#6, OC#2, Insula, and CgG#2. Such a precise quantitative perspective on interactions between various brain sub-structures has not been previously possible. Table S3 contains a number of interesting insights, as examples, observe that cingulate cortex is very tightly interconnected with frontal lobe, that frontal lobe has the highest average in-degree amongst all enumerated structures, and that a region in insula sends out, on an average, two connections for every connection that it receives. Further, various cortical constituents are highly interconnected and are also intertwined with diencephalon (DiE) and basal ganglia (BG). A divide-and-conquer approach to studying each constituent part in isolation by ignoring the interrelationships is unlikely to be fruitful. The brain is truly a complex system for integrating information that is substantially more than a simple sum of its parts, and thus must be studied as a whole. The behavior of the brain apparently emerges via non-random, correlated interactions between parts, which is a key characteristic of organized complexity [26]. Such complex systems are often amenable to computer modeling and simulation thus pointing to a prosperous future for computational neuroscience. Computing k -Cores. Suppose that we are given an undirected graph

with vertex set V and edge set E. For k ≥ 1, a k-core is the maximal subset Vk of V such that every vertex in Vk has at least k connections with other vertices in Vk . The cores are recursively computed as folModha & Singh

lows. Set V0 = V . Now, to obtain Vk , k ≥ 1, start from Vk−1 and while there remain any vertices with less than k connections remove ˆ ≥ 1 such that Vˆ them. The process stops at some k k+1 = ∅. Increasing k amounts to recursively peeling off the underlying network to reveal progressively more closely connected subgraphs. The cores are naturally nested, that is, V0 contains V1 which contains V2 , and so on, and, hence, we may think of the cores as constituting a hierarchy. The innermost core Vkˆ is the top of this hierarchy. Define shells as follows: ˆ Sk = Vk \ Vk+1 , 0 ≤ k ≤ k, where \ represents set difference operator. The shell Sk is simply those vertices that are in Vk but not in Vk+1 . For k ≥ 0, let Ek ⊂ E denote the set of edges between vertices in Vk . We now describe a formal algorithm for computing the cores and shells that yields deeper insight into the finer structure of each shell. The algorithm starts from (Vk , Ek ) and yields (Vk+1 , Ek+1 ) as well as a finer decomposition of Sk into a sequence of disjoint sub-shells Fk,1 , Fk,2 , . . . , Fk,mk . For a > b, each element of the set Fk,a has more edges to Vk+1 than each element of the set Fk,b .

area 19) roughly map, assuming homology between human-macaque [29, 30, 31, 32, 33, 34], to 7#1, 7b, 7a, IPL, PF#1, PG#1, S2, 2#1, STS, TPO, TPOc, 6#1, 6D, 6M, 6V, F2, F7, F6, F3, SMAr, F4, F5, PrCO, 46, 46d, 46v, PS, Ig#1, Idg, Ia#2, Iai, Iam, and Iapm in the innermost core. Similarly, the task-negative network consists of Brodmann regions 31, 30, 39, 32/10, 8, 20/21, and 35 which (with the exception of area 39) roughly map to PECg, PGm, SPL, PEm, PEc#1, TE, AITv, PIT, AITd, 35, ENT, PrS, TH, TF, 32, 10, 10o, FEF, 45, 8A, 8, 8B, and 31 in the innermost core. In addition to these networks, the innermost core contains portions of prefrontal cortex (14, 13, 9, 12, 11, 14r, 13a, 13L, 13M, M9, 12l, 12m, 12o, 12r, 11l, 11m), cingulate cortex (25, 24, 23, 24a, 24b, 24c, 23c), thalamus (MD, Pul#1, MDmc, PL#3, Pul.o, PM#3, Cl#2, CM#2, Pcn, Li, VA, MDpc, VAmc, VLo, VPL), basal ganglia (SI#2, B#2, L#2, Cd, ABmg, Abpc, Bi, Bla, Lvl, Lv, Pu r, Ldi), temporal lobe (Tpt, A1, TAa, ST1, ST2, ST3, TG, TPPro, 36, 36c, 36r), parietal lobe (LIP, MIP), primary motor cortex (M1, M1-FL), and visual cortex (V4). All these vertices are shown in Figure S33.

Input: k, Vk , Ek 1. Initially, set Vk+1 = Vk , Ek+1 = Ek . Set mk = 0. 2. while (some vertex in (Vk+1 , Ek+1 ) has degree less than k + 1) (a) Set mk = mk + 1. (b) Let Fk,mk denote the set of all vertices in (Vk+1 , Ek+1 ) that have degree less than k + 1. (c) Vk+1 = Vk+1 \ Fk,mk . Let Ek+1 denote the set of edges between vertices in Vk+1 . endwhile Output: Vk+1 , Ek+1 , mk , {Fk,1 , Fk,2 , . . . , Fk,mk }, Sk = Vk \ mk Vk+1 = ∪n=1 Fk,n . ˆ = 29. FigApplying the above algorithm to our network yields k ure S34 shows that the core size decreases linearly with increasing k. We enumerate all shells {Sk }29 k=0 and all finer sub-shells in Table S5. Finally, using a technique similar to that in [27], we visually illustrate the entire k-core decomposition in Figure S31. Coreness Centrality. Coreness uncovers a sequence of progressively

more densely interconnected sub-networks. In the process, it implicitly defines a measure of topological centrality on the vertices. For example, for our network the innermost ring in Figure S31 is most central and the outer most ring is least central. Table S5 can be interpreted as listing the vertices in the ascending order of coreness centrality, where all vertices within a fine shell are assigned the same coreness centrality value. The innermost fine shell F29,14 has the highest coreness centrality, and, once again, contains 8 brain regions in prefrontal cortex (32, 8B, 14, 10, 9, 11, 46, 12o) from a total of 11, thus corroborating Table 1 of the main text. A limitation of Table 1 is that it limits attention to top ten brain regions. Figure S31 can be used to overcome this limitation. For example, keeping vertex position identical to that in Figure S31, Figure S32 colors the vertices according to betweenness centrality where hot colors represent high betweenness centrality and cool colors indicate low betweenness centrality. It can be clearly seen that hot colors are concentrated in the inner rings. Task-Positive and Task-Negative Networks The task-positive net-

work [28] consists of Brodmann regions 7, 7/40, 19, 6, 6/32, 46, 19/37, and Insula/frontal operculum which (with the exception of

5

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Stability of the Innermost Core Given the structural and functional

importance of the innermost core, we now show that it is stable with respect to modest changes in the underlying network. We intuitively explain the basic notion of stability. Let a > b, v ∈ Va and u ∈ Vb . Then, removing a connection between v and u can lead both vertices to move to outer cores. Conversely, adding a connection between v and u may lead for u to move to an inner core but cannot change the position of v. Thus, for vertices in the innermost core, it is most interesting to study deletions of connections to other vertices in the innermost core, whereas for vertices outsides the innermost core (that is, in the crust), it most interesting to study additions of connections to vertices in the innermost core. In Table S6, we enumerate all 383 vertices in decreasing order of the number of connections to the innermost core. We distinguish 122 members of the innermost core by color coding them. The first column shows number of connections to the innermost core. For example, area 46 has 129 connections to the innermost core. For the 122 members of the innermost core, the second column shows how many connections can be safely deleted without removing the associated vertex from the innermost core. For example, we can safely delete upto 100 connections between area 46 and the innermost core, and it will still remain a member of the innermost core. The area 24 has 111 connections to the innermost core and, so, we can delete 82 of these connections while still retaining it in the innermost core. As we go down the table, it can be seen that brain regions Pul#1, SPL, PrS, and SMAr have exactly 29 connections to the innermost core, and, hence, removing even a single connection from them to the innermost core will remove them from the innermost core. Thus, against random deletions of connections, we can say that area 46 is more stable member of the innermost core, than area 24, which in turn is significantly more stable than Pul#1, SPL, PrS, and SMAr. For the remaining 261 vertices of the crust, the first column still shows number of connections to the innermost core, but the second column now shows how many connections need to be added between a vertex and the innermost core for the vertex to become a member of the innermost core. The second column uses negative numbers – since these connections have to be added. For example, any of the brain regions V2, Pf#2, Ld#2, TFL, PGa, and VLc can be promoted to the innermost core by simply adding one connection between itself and the innermost core. In summary, modest changes in the database may move individual affected brain regions up or down in the core hierarchy, but cannot substantially change the global core structure.

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1. Kaiser M, Hilgetag CC (2006) Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2:805-815. 2. http://www.cocomac.org (2000). ¨ 3. Stephan K, Zilles K, Kotter R (2000) Coordinate-independent mapping of structural and functional data by objective relational transformation (ORT). Phil. Trans. R. Soc. Lond. B 355:37-54. ¨ 4. Kotter R, Wanke E (2005) Mapping brains without coordinates. Phil. Trans. R. Soc. Lond. B 360:751-766. ¨ 5. Kotter R (2004) Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database. Neuroinformatics 2:127-144. 6. Stephan KE, et al. (2001) Advanced database methodology for the collation of connectivity data on the macaque brain (CoCoMac). Phil. Trans. R. Soc. Lond. B 356:1159-1186. 7. Pandya DN, Seltzer B (1982) Intrinsic connections and architectonics of posterior parietal cortex in the rhesus monkey. J. Comp. Neurol. 204:196-210. 8. Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in primate cerebral cortex. Cereb. Cortex 1:1-47. 9. Rockland KS, Drash GW (1996) Collateralized divergent feedback connections that target multiple cortical areas. J. Comp. Neurol. 373:529-548. 10. Paxinos G, Huang XF, Toga AW (1999) The Rhesus Monkey Brain in Stereotaxic Coordinates (Academic Press). 11. Paxinos G, Huang XF, Petrides M, Toga AW (2008) The Rhesus Monkey Brain in Stereotaxic Coordinates, Second Edition (Academic Press). 12. Tollis IG, Di Battista G, Eades P, Tamassia R (1998) Graph Drawing: Algorithms for the Visualization of Graphs (Prentice Hall). 13. Lamping J, Rao R, Pirolli P (1995) A Focus+Context Technique Based on Hyperbolic Geometry for Visualizing Large Hierarchies (ACM/SIGCHI), pp 401–408. 14. Gonzalez RC, Woods RE (2008) Digital Image Processing (Addison-Wesley Pub (Sd)), 3 edition. 15. Itten J (1961) The Art of Color (John Wiley & Sons, Inc, New York). 16. Holten D (2006) Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data. IEEE Trans. Vis. Comput. Graph. 12:741-748. 17. Ungerleider LG, Mishkin M (1982) in Analysis of visual behavior, eds Ingle DJ, Goodale MA, Mansfield RJ (MIT Press, Cambridge, MA), pp 549-586.

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18. Sherman SM, Guillery RW (2006) Exploring the thalamus and its role in cortical function (The MIT Press, Cambridge, MA). 19. Schmahmann JD, Pandya DN (2006) Fiber Pathways of the Brain (Oxford University Press). 20. Milgram S (1967) Small-world problem. Psychology Today 1:61-67. 21. Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393:440-442. 22. Sporns O, Zwi J (2004) The small world of the cerebral cortex. Neuroinformatics 2:145-162. 23. Tononi G, Edelman GM (1998) Consciousness and complexity. Science 282:18461851. 24. Koch C, Laurent G (1999) Complexity and the nervous system. Science 284:96-98. 25. Sherman SM, Guillery RW (1996) Functional organization of thalamocortical relays. J Neurophysiol. 76:1367-1395. 26. Weaver W (1948) Science and complexity. American Scientist 36:536-536. 27. Alvarez-Hamelin JI, Dall’Asta L, Barrat A, Vespignani A (2005) Large scale networks fingerprinting and visualization using the k-core decomposition. 28. Fox MD, et al. (2005) The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad Sci U S A 102:9673-9678. 29. Van Essen DC (2004) in The Visual Neurosciences, eds Chalupa L, Werner J (MIT Press), pp 507-521. 30. Orban GA, et al. (2003) Similarities and differences in motion processing between the human and macaque brain: evidence from fMRI. Neuropsychologia 41:17571768. 31. Astafiev SV, et al. (2003) Functional organization of human intraparietal and frontal cortex for attending, looking, and pointing. The Journal of Neuroscience 23:46894699. 32. Orban GA, Van Essen DC, Vanduffel W (2004) Comparative mapping of higher visual areas in monkeys and humans. Trends in Cognitive Sciences 8:315-324. 33. Orban GA, et al. (2006) Mapping the parietal cortex of human and non-human primates. Neuropsychologia 44:2647-2667. 34. Vincent JL, et al. (2007) Intrinsic functional architecture in the anaesthetized monkey brain. Nature 447:83-86.

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Fig. S1. Connectivity of the largest previous long distance network [1] within our visualization framework. The network consists of 95 vertices and 2,402 edges. By comparing this network to our network in Figure 1 of the main text, the richness of our data becomes apparent.

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AP84-TE

/ BP82-46

PG91b-IT o

SP89a-46

(a)

/ FV91-V4 == == == == == == == ==

FV91-V1 ^=

/ FV91-TF

RV99-TF

/ RV99-CA1

FV91-TH BR98-TH o

BR98-CA1

(b) Fig. S2. Connectivity between brain regions by different tracer injection studies. The notation x → y means that there is a connection from brain region x to y . By establishing an equivalence between AP84-TE and PG91b-IT and between BP82-46 and SP89a-46, the first example can be used to infer that there is a reciprocal connection between inferotemporal area, which is often denoted as either TE or IT, and prefrontal area 46. Similarly, by establishing equivalences between regions with the same acronym (shown via dotted enclosing rectagles), the second example can be used to infer that there is a short circular path containing V1 and CA1 subfield in the hippocampus, namely, V1 → V4 → TF → CA1 → TH → V1.

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Fig. S3. Five examples of conflict between I and L relations. Sub-matrices of I+ and L+ corresponding to the conflict are shown for each case. In each matrix the entries in black are the original relations while entries in blue are the relations because of transitivity. Conflicts in each case are shown by underlining the relevant entry.

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I+

J+ I

J L

L+ Fig. S4. The binary relations I and L are transitive, and let I+ and L+ denote the respective transitive closures. We define the conflict relation as the intersection between I+ and L+ . We compute a subset J of I such that intersection of J+ and L+ is empty. This is a conflict-free identity relation, and can be safely used for merging.

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DiE

FL#2

Pl#6 CgG#2 Ins

TL#2 OC#2 BG 0

50

100

150 200 nz = 276

250

300

350

Fig. S5. A matrix visualization of 143 remaining overlap relations in our hierarchical brain map. Rows and columns of the matrix correspond to the brain regions in Table S1 in the same order. The symbol “•” denotes the presence of an overlap relation between two corresponding brain regions. Given the symmetry of overlap relation, the lower and upper triangular parts are transposes of one another. For ease of visualization, we have divided the matrix into big container regions diencephalon (DiE), basal ganglia (BG), occipital lobe (OC#2), temporal lobe (TL#2), insula (Insula), cingulate cortex (CgG#2), parietal lobe (Pl#6), and frontal lobe (FL#2). Although, brain regions in FL#2 have overlap with brain regions CgG#2 and brain regions TL#2 has some overlap with brain regions in OC#2, Pl#6, and Insula, typically, overlap is limited to two brain regions within a container.

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Fig. S6. Hierarchical macaque brain map consisting of 383 regions in brain (Br) that is divided into cortex (Cx), diencephalon (DiE), and basal ganglia (BG). Further, cortex is divided into temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2), and so on. Each brain region is represented via its acronym or abbreviation enclosed in a small colored rectangle. The acronyms are consistent with CoCoMac, which explains somewhat mechanical abbreviations such as CgG#2. The brain regions in the three outermost circles are leaves that cannot be further subdivided. Legend: We have used a color wheel for better discrimination amongst brain regions. For the leaf brain regions in the two outermost circles, we have rotated the color wheel by 120 degrees and 240 degrees. Table S1 enumerates the entire hierarchical brain map and provides a complete index to acronyms of the brain regions, and has been color coded for wider accessibility. See Figures S7-S14 that zoom into the hierarchical brain map and Figure S15 that uses an alternative color scheme.

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#2 OC

Ins ula

TL #2

BG

CgG#2

Cx Br

Pl

#6

DiE

2 FL# Fig. S7. Hierarchical decomposition of brain (Br) into cortex (Cx), diencephalon (DiE), and basal ganglia (BG), and cortex into temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2). The descendants of DiE, BG, TL#2, FL#2, Pl#6, OC#2, Insula, and CgG#2 are not shown here, but are shown in subsequent figures.

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MS Tp MS Td

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Fig. S8. Hierarchical decomposition of temporal lobe (TL#2).

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DL

r

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Fig. S9. Hierarchical decomposition of occipital lobe (OC#2).

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Bl

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c

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Fig. S10. Hierarchical decomposition of basal ganglia (BG).

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Hyp

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c Fig. S11. Hierarchical decomposition of diencephalon (DiE).

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Fig. S12. Hierarchical decomposition of frontal lobe (FL#2).

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PECg

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Fig. S13. Hierarchical decomposition of parietal lobe (Pl#6).

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Iam

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Fig. S14. Hierarchical decomposition of insula (Insula) and cingulate cortex (CgG#2).

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Modha & Singh

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Fig. S15. An alternative visualization where the text labels have been drawn in black on light background, and in white on dark background, in order to improve the accessibility of the figure.

21

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Fig. S16. Example to show visualization of network edges, and effect of bundling. Areas Bla and MB are in amygdala, and areas MD and MDmc are in thalamus. Three long distance connections, from Bla to MDmc, MB to MDmc, and MB to MD, are shown. The control polygon of the connection between Bla and MDmc is through nodes, Bla, B#2, Amyg, BG, Br, Die, Tha, MD, and MDmc. It is easy to observe that the control polygon for the connection between MB and MDmc is very similar, in-fact it differs only in the last control point, MB instead of Bla, and similarly for the connection between MB and MD. Thus tracing from the areas in amygdala, splines of all three connections would bundle together left of the least common control point, B#2, rise up to the least common ancestor, Br, and then come down to Tha, where just above MD, the splines would split, and end at their respective destinations, MD and MDmc. The amount of bundling is controlled by the bundling factor β . Four different value of the bundling factor β are shown. (a) β = 0; (a) β = 0.5; (a) β = 0.8; and (a) β = 0.993. It can be seen that as bundling factor increases, more clarity ensues.

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Modha & Singh

(a)

(b)

(c)

(b)

Fig. S17. Long distance network in the macaque brain consisting of 383 hierarchically organized brain regions and 6,602 directed connections shown with four different value of the bundling factor β . (a) β = 0; (a) β = 0.8; (a) β = 0.95; and (a) β = 0.993. It can be seen that as bundling factor increases, more clarity ensues. For all other figures in this paper, the bundling factor has been chosen to be 0.993.

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Modha & Singh

(a)

(b)

(c)

(d)

Fig. S18. To demonstrate comprehensiveness, the figure illustrates that sub-networks corresponding to four classical fiber systems are all contained within our network. (a) The fiber system of [8] illustrating connectivity of visual cortex with temporal lobe, parietal lobe, and frontal lobe. (b) The fiber system of [17] illustrating the dorsal (“where”) pathway from occipital lobe to parietal lobe and the ventral (“what”) pathway from occipital lobe to temporal lobe. (c) Superior longitudinal fasciculus [19] between parietal and frontal lobes that mediates the initiation of motor activity as well as visual awareness/attention. (d) Thalamocortical Relays [18] illustrating the extensive coupling between cortex and thalamus. To further emphasize the richness of our network, Figures S19, S20, and S21 illustrate sub-networks corresponding to other classical fiber systems described in [19], namely, arcuate fasciculus, cingulum bundle, extreme capsule, frontooccipital fasciculus, inferior longitudinal fasciculus, middle longitudinal fasciculus, uncinate fasciculus, connectivity between cortex and striatum/claustrum, connectivity between amygdala and cortex, and connectivity between amygdala and diencephalon.

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Fig. S21. Sub-networks corresponding to various classical fiber systems in the brain: (a) amygdala and cortex, (b) amygdala and diencephalon.

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0.9

Probability(degree ≥ x)

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x Fig. S22. The linear-linear plot shows the empirical complementary cumulative degree distribution (circles) and the complementary cumulative distribution of the maximum entropy exponential distribution fit (dashed line), λ−1 exp(−x/λ), λ = 27.2, over the entire range of data.

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2

Number of connections reported for a brain region in CoCoMac

10

1

10

0

10 0 10

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10 Number of times a brain region is studied in CoCoMac

2

10

Fig. S26. A plot of the number of times a brain region is studied, against its number of connections as reported in CoCoMac. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

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2

Degree of a brain region in our network

10

1

10

0

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1

10 Number of times a brain region is studied in CoCoMac

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Fig. S27. A plot of the number of times a brain region is studied in CoCoMac, against its degree in the final network. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

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2

Degree of a brain region in our network

10

1

10

0

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1

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10 10 Number of connections reported for a brain region in CoCoMac

Fig. S28. A plot of the number of connections of a brain region reported in CoCoMac, against its degree in the final network. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

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4

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10

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Fig. S29. A plot of the degree of a brain region in the final network, against its betweenness centrality. The red crosses correspond to brain regions in prefrontal cortex.

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Fig. S30. The innermost core for the undirected version of our network. The innermost core is a central sub-network that is far more tightly integrated than the overall network, information likely spreads more swiftly within the innermost core than through the overall network, the overall network communicates with itself mainly through the innermost core, and the innermost core contains major components of the task-positive and task-negative networks derived via functional imaging research [28].

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-c

c

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d

a

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ngli

1

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30

36

o Pr TP

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b

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20 CIT

CITv

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Ial

26

Lo

sa

PrS

EC

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l

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A2

CA1

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ER

ula

paAlt

L#1

1

r

oD

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AL#4 STG

paAc

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pr

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s. Pro

v

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g STP

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m

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dg ag

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28

36

d

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TP

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p

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ita

e

PH

CA3

DG

#2

21

Pa#2

CITd

Sb

Su EL

TP Pe

cip

r

TPOi

po Tem

Fron tal

Lob

e

Fig. S31. Starting from the center, the innermost 14 rings correspond to the fine shells of the innermost core. The finest shell F29,14 is at the center, followed by F29,13 , and so on, until F29,1 . The next 28 rings correspond to the shells S28 , S27 , . . . , S1 , in that order from center to the periphery. The angular position of each vertex within a ring is the same its angular position in Figure S6. The color of each vertex is the same as its color in Figure S6.

37

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Modha & Singh

obe ral L

Oc

VO T

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t

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sa

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AL#4 STG

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pr

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g STP

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p

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cip

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tal

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Fig. S32. The vertex positions are identical to that in Figure S31. The vertices are colored according to betweenness centrality where hot colors represent high betweenness centrality and cool colors indicate low betweenness centrality. It can be clearly seen that hot colors are concentrated in the inner rings.

38

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Modha & Singh

TPOc

PIT

AITd

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ula

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e

ulat

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2

sa

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pc

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c

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al

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10

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M

Dm

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r

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1

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PM

M

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2#

1

6M

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e

Fig. S33. Vertices in the innermost core are shown. Vertices corresponding to the task-positive network are shown in red, vertices corresponding to the task-negative network are shown in blue, and the remaining vertices in the innermost core are shown in yellow. The vertex positions are identical to that in Figure S6.

39

www.pnas.org/cgi/doi/10.1073/pnas.1008054107

Modha & Singh

Fig. S34. A graph of how the core size decreases linearly with increasing k . A linear least-squares regression fit is shown with (core size) = −8.0476∗k+380.9379.

40

www.pnas.org/cgi/doi/10.1073/pnas.1008054107

Modha & Singh

Table S1: Hierarchical brain map in depth-first order Level

Acronym

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

0 1 2

Br

Brain according to GM-Definition Diencephalon according to GM-Definition Hypthalamus [ ALH APH DMH Hce1 Hce2 SMH hy ] Thalamus Anterior nuclei of the thalamus [ LN ] Laterodorsal nucleus (thalamus) [ Cld ] Nucleus anterior ventralis thalami Nucleus anterior medialis thalami [ AMdc ] Nucleus anterior dorsalis thalami Midline nuclei of the thalamus [ Pac#2 sPFmc sPFpc ] Nucleus reuniens thalami [ Rv ] Nucleus parataenialis thalami Nucleus paraventricularis thalami, pars anterior [ PAm#2 PAp Pa#3 ] Nucleus centralis thalami [ Ce#2 CeM#2 ] Nucleus centralis latocellularis thalami Nucleus centralis intermedialis thalami Nucleus centralis inferior thalami Nucleus centralis densocellularis thalami [ ND ] Metathalamus (Geniculate Nucleii) Corpus geniculatum mediale [ AD#3 GM GMpc MC MGM MGN MGad ] [ MGpd PD#3 V Z ] dorsal Lateral geniculate nucleus [ 2#2 DLG DLGN LGN#1 LGN 0 LGN 1 ] [ LGN 2 LGN 3 LGN 4 LGN 5 LGN 6 LGN il LGN il-z ] [ LGN k1 LGN l LGN mc LGN mc-il LGN mc-l LGN pc LGN pc-il ] [ LGN pc-l LGN s LGil LGm LGp LGs ] Intralaminar nuclei of the thalamus Nucleus parafascicularis thalami Nucleus paracentralis thalami [ Pc#3 ] nucleus centrum medianum (thalamus) [ CnMd ] Nucleus centralis lateralis thalami Nucleus centralis superior lateralis thalami Nucleus centralis superior thalami Massa intermedia Posterior Nucleii of Thalamus [ Po#5 SM ] Nucleus suprageniculatus thalami Nucleus limitans thalami [ Lim ] Nucleus reticularis thalami [ NRT AnteriorPole R#4 RT#2 ] Nucleus pulvinaris thalami [ PLe ] Nucleus pulvinaris inferior thalami [ Pul.i ] Nucleus pulvinaris inferior thalami, shell of the lateral subdivision Nucleus pulvinaris inferior thalami, posterior subdivision Nucleus pulvinaris inferior thalami, pars medialis Nucleus pulvinaris inferior thalami, lateral subdivision [ PIcl ] Nucleus pulvinaris inferior thalami, central subdivision [ PIcm ]

0 4 10

0 0 25

3 1 9

Number of Connections reported 0 0 50

5 8

1 8

2 6

1 11

9

14

17

15

11 10

7 22

15 16

7 23

9 7

5 12

10 14

5 18

11

24

14

26

10 9

7 13

5 13

7 16

8

4

4

4

11 10 9 11

11 7 11 17

7 5 8 10

12 7 11 19

8 10

0 23

1 59

0 49

9

10

78

86

7 11 10

14 32 50

5 13 14

14 33 69

9

43

24

71

8 11 10 9 8

50 28 5 3 2

21 8 6 3 10

74 31 5 3 3

11 10

29 43

15 13

33 46

9

31

27

32

7

44

32

137

8

26

43

53

11 10 9 11

2 4 7 9

3 8 9 8

2 4 7 10

10

9

9

9

2 3

DiE Hyp Tha AN

4

LD#1

4 4

AV AM#1

4 3

AD#1 ML

4

Re

4 4

PT#2 PAa

4

C#4

5 5 5 5 3 4

Clc Cim Cif Cdc GN MG

4

LGN

3 4 4

IL#2 Pf#2 Pcn

4

CM#2

4 5 5 3 3

Cl#2 Csl Cs#2 MI#1 PN

4 4

SG Li

3

Ret

3

Pul#1

4

PI#3

5 5 5 5

PIl-s PIp PIm PIl

5

PIc

continued on next page...

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...continued from previous page

Level

Acronym

4

PM#3

5 5 4

PMm PMl Pul.o

4

PL#3

5 5 5 5 3 4

PLa#1 PLd PLvl PLvm MD MDdc

4 4 5 5 4

MDcd MDl MDpc MDmf MDmc

5 5 3

MDpm MDfi VN

4 4 5 5 5

X VP#2 VPS VPI VPM

5

VPL

6 6

VPLo VPLc

4 5 5 5

VL VLm VLps VLo

5

VLc

4 5 5 5 1 2 3 3 4

VA VApc VAdc VAmc Cx FL#2 belt sm Pfc PFCorb

5

14

6 6 5

14O 14r OFap

5 6

OFO ProM#2

6

Gu

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

Nucleus pulvinaris medialis thalami [ PMm-c Plm#2 Pul.m mPul ] Nucleus pulvinaris medialis thalami, medial division Nucleus pulvinaris medialis thalami, lateral division Nucleus pulvinaris oralis thalami [ PO#3 Pa#4 Pla#2 ] Nucleus pulvinaris lateralis thalami [ PLb PLi Pll#2 Pul.l ] Nucleus pulvinaris lateralis thalami pars alpha Nucleus pulvinaris lateralis thalami, dorsal division Nucleus pulvinaris lateralis thalami pars ventrolateralis Nucleus pulvinaris lateralis thalami pars ventromedialis Nucleus medialis dorsalis thalami Nucleus medialis dorsalis thalami, pars densocellularis [ MDd ] Nucleus medialis dorsalis thalami, pars caudodorsalis Nucleus medialis dorsalis thalami, pars lateralis Nucleus medialis dorsalis thalami, pars parvocellularis Nucleus medialis dorsalis thalami, pars multiformis Nucleus medialis dorsalis thalami, pars magnocellularis [ MDm ] Nucleus medialis dorsalis thalami, pars paramediana Nucleus medialis dorsalis thalami, pars fibrosa Ventolateral Nucleii of Thalamus [ VM#2 VMH ] Area X (thalamus) Nucleus ventralis posterior Ventroposterior superior nucleus thalami Nucleus ventralis posterior inferior thalami Nucleus ventralis posterior medialis thalami [ VPM CP VPM UL VPMpc n.vent.post.med. ] Aentral posterior lateral nucleus (thalamus) [ LP VLp ] Nucleus ventralis posterior lateralis thalami, pars oralis Nucleus ventralis posterior lateralis thalami, pars caudalis [ VPLc core h VPLc shell l ] ventral lateral nucleus (thalamus) Nucleus ventralis lateralis thalami, pars medialis Nucleus ventralis lateralis thalami, pars postrema Nucleus ventralis lateralis thalami, pars oralis [ VLa ] Nucleus ventralis lateralis thalami, pars caudalis [ VLc-VPLo VLcc VLcr ] ventral anterior nucleus (thalamus) [ VAvm ] Nucleus ventralis anterior thalami, pars parvocellularis Nucleus ventralis anterior thalami, pars densocellularis Nucleus ventralis anterior thalami, pars magnocellularis GM-CerebralCortex FrontalLobe according to GM-Definition belt line of the sensorymotor system according to CP99 [ root sm ] Prefrontal Cortex Orbital prefrontal cortex [ OF OFdg OFg OPro OrbPro ] Orbitofrontal area 14 [ M14 ] Orbital part of area 14 Rostral area 14 Orbitofrontal cortex, agranular periallocortical [ OFa-p PAll#1 ] Orbitofrontal opercular area Pro motor area [ proM#1 ] Gustatory cortex

8

85

41

Number of Connections reported 114

9 11 10

7 8 45

1 1 26

7 8 54

8

50

44

84

9 11 10 9 7 11

2 5 5 5 106 21

3 1 1 3 29 8

17 5 5 5 200 23

10 8 9 11 8

5 6 38 17 39

1 2 10 8 12

9 6 43 18 57

10 9 6

10 21 7

1 1 7

10 22 7

11 7 10 9 11

28 1 7 12 20

10 4 1 16 32

49 1 8 16 40

8

56

39

88

10 9

20 29

11 16

48 54

8 11 10 9

18 25 21 34

9 10 7 11

19 43 25 68

11

32

15

70

8

33

18

41

10 9 11 1 4 10

21 7 38 0 0 22

8 1 13 1 1 2

38 7 51 0 0 22

5 7

0 10

2 12

0 14

8

111

34

158

9 11 10

5 66 8

2 3 12

6 77 8

8 9

2 31

6 8

2 33

11

22

16

25

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Level

Acronym

Full Name [Merged Brain Regions]

5

13

6 6 6 4 4 5

13L 13M 13a 32 FD#1 10

6 6

10m 10v

6

10d

6 5 6

10o 12 12o

6 6

12m 47/12

6 6

12r 12l

5 6 6 5

11 11l 11m 9

6 6 6 5

L9 M9 D9 46

6

46v

6

46d

6 6 6 6 6 7 7 4

PS 46f 46vr 46dr 9/46 9/46v 9/46d 8

5 6

FEF 45

7

45A

7 6

45B 8A

7 7 5

8Ad 8Ac

3 4

8B 6#1 6V

[ G#1 G#2 G#3 ] Orbitofrontal area 13 [ FF ] Orbitofrontal area 13, lateral part Orbitofrontal area 13, medial part Orbitofrontal area 13a [ 13b ] Area 32 Prefrontal area FD Area 10 [ M10 ] Medial area 10 Ventral area 10 [ V10 ] Dorsal area 10 [ D10 ] Orbital area 10 Area 12 Orbital area 12 [ O12 ] Medial area 12 Prefrontal area 47/12 [ 47/12L 47/12O ] Rostral area 12 Lateral area 12 [ 12vl L12 ] Area 11 Lateral area 11 Medial area 11 Area 9 [ 9d 9m ] Lateral area 9 Medial area 9 dorsal area 9 Cortical area 46 [ 46inf 46p 46sup FDdelta ] Ventral area 46 [ V46 V46r ] Dorsal area 46 [ D46 D46r ] Principal Sulcus Area 46 (fundus of the principal sulcus) Area 46 (ventral rim of the principal sulcus) Area 46 (dorsal rim of the principal sulcus) Cortical area 9/46 Cortical area 9/46v Cortical area 9/46d Area 8 [ 8As ] Frontal eye field Cortical area 45 [ 8v FDgamma V8#2 ] Cortical area 45A [ 45a+8Ar 8Ar ] Cortical area 45B Area 8A [ 8Av ] Dorsal portion of area 8A Caudal area 8A Area 8B [ 8Bd 8Bm 8d D8 ] Area 6 [ 6a-alpha 6a-beta 6b FB PM#4 ] Area 6 (ventral part) [ PMCvl PMv V6#2 vPmC ]

Ring Number

Degree

Number of times studied

Number of Connections reported

8

129

36

203

10 9 11

47 39 130

5 5 15

55 55 223

10 6 8

159 33 100

36 2 39

226 42 154

9 11

21 7

4 3

24 10

10

3

3

7

9 8 11

44 90 135

2 31 10

52 136 174

10 9

54 24

2 7

69 27

11 10

38 123

2 9

47 155

8 9 11 8

127 39 63 125

33 4 4 53

207 52 76 219

10 9 11 7

7 43 26 211

1 1 1 46

9 51 30 366

10

89

12

120

9

45

11

58

11 10 9 11 8 10 9 6

70 2 5 4 0 13 30 54

1 1 3 2 2 3 3 32

72 2 5 4 0 15 36 85

7 8

67 79

13 32

93 100

11

31

9

43

10 8

12 97

5 17

14 133

9 11 10

29 6 89

3 4 23

32 7 116

6

70

50

114

8

74

12

258

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...continued from previous page

Level

Acronym

5

F5

5

PrCO

5

4c

5 5

6Vb 6Va

5

F4

4 4 4

44 6b-beta 6D

5

F7

5

F2

4

6M

5

F3

6 6 5 5 5

SMAr SMAc M2-HL M2-FL F6

3

M1

4

M1-FL

4

MI-of

4 4 4

4b 4a MI-body

4

M1-HL

2 3

Pl#6 S1

4

PC#1

5

1#1

5

2#1

4 5 5 3 4 4 3 3

3#1 3b 3a S2 SII-f CMA#2 belt s PR#4

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

Agranular frontal area 5 (= rostral ventrolateral premotor area) [ 6VR FCBm MLA PMv-r PMvr ] Precentral opercular area [ 6b-alpha ] Motor area 4c [ Postarc ] Premotor area 6Vb Premotor area 6Va [ 6Vam 6val ] Agranular frontal area 4 (= caudal ventrolateral premotor area) [ 6VC FBA PMv-c PMvc ] Cortical area 44 Premotor area 6b-beta Premotor area 6 (dorsal part) [ 6Ds D6 PMd dPmC ] Agranular frontal area 7 (= rostral dorsolateral premotor area) [ 6DR F7-SEF F7-nonSEF PMd-r PMdr SEF rPMd ] Agranular frontal area 2 (= caudal dorsolateral premotor area) [ 6DC F2d F2vr PMd-c PMdc Pmdp cPMd ] Medial premotor area 6M [ M2 M2-FA MII MII-arm MII-face MII-leg MII-trunk PMCm ] [ SMA SMA-of TMA ] Agranular frontal area 3 (= SMA-proper) [ F3-arm F3-axial F3-leg SMA-proper ] SMA - rostral part SMA - caudal part Supplementary motor cortex M2, hindlimb area Supplementary motor cortex M2, forelimb area Agranular frontal area 6 (= pre-SMA) [ F6-arm F6-axial pre-SMA preSMA ] Primary motor area [ 4#1 F1 FA MI#3 ] Primary motor cortex M1, forelimb area [ 4-fl 4-hand ARM F1-arm MI-arm MI-finger MI-forelimb ] [ MI-hand MI-hand-arm ] orofacial representation in MI [ 4-mouth F1-face M1-FA ] Motor area 4b Motor area 4a body representation of MI as defined in KSI03 [ M1-AX MI-neck MI-trunk ] Primary motor cortex M1, hindlimb area [ F1-leg MI-hindlimb MI-leg MI-toe ] ParietalLobe according to GM-Definition Primary somatosensory cortex [ 1-2 SI#1 SI-arm SI-finger SI-leg SI-neck SI-trunk ] [ SI D1 SI D1p SI T3-4 SI Trnk ] Primary sensory area PC [ 3b/1 ] Area 1 [ 1 O SI Arm SI Hnd SI LL SI Max SI T1 SI T4-5 ] [ SI UL SI ULp ] Area 2 [ 2 D2-5 SI D2 SI D2-3 SI D2-3p SI D2-4 SI D3-4 SI D3-4p SI D3-5 ] Area 3 Postcentral area 3b [ 3b CP 3b LL 3b UL SI Leg ] Postcentral area 3a Secondary somatosensory cortex [ 43 PCop SII SII-fl SII-h SII-hl SII-sub ] face representation in SII as defined in DLRPK03 Cortical masticatory area [ CMAaAd CMAp ] belt line of the sensory system according to CP99 rostroventral parietal area as defined in DLRPK03

9

88

16

Number of Connections reported 137

11

36

16

51

10

17

7

20

9 11

20 23

9 10

23 25

10

48

13

84

9 11 8

6 2 82

4 2 22

6 2 151

10

124

28

245

9

88

22

183

7

93

50

188

8

69

15

162

11 10 9 11 10

41 2 7 6 57

1 1 1 1 17

43 2 15 13 108

8

96

57

246

9

86

16

164

11

24

5

34

10 9 11

2 2 21

1 1 4

2 2 28

10

31

6

44

5 7

0 31

1 39

0 68

8

14

3

18

9

49

46

149

11

54

43

153

8 10

27 32

14 28

33 75

9 8

35 81

26 56

67 206

11 10

5 2

3 4

13 2

9 11

13 19

1 6

21 54

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44

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...continued from previous page

Level

3

Acronym

Full Name [Merged Brain Regions]

7#1

4 4 4

PFop PP PGop

4

IPL

5 6 6 5 6 6 3 4

7a PG#1 Opt 7b PFG#1 PF#1 PCip LIP

5

LIPe

5

LIPi

4

VIP

4 4 4

PIP#1 AIP MIP

3 4

PCd#2 SPL

5

PEm

5 5

5 Foot PEc#1

4 5

PCm PGm

5 5

31 PECg

2 3

CgG#2 24

4

24c

4

24d

4 4 3

24b 24a 23

4

23c

4 4 4 3

23b TSA 23a

4 5 5

26 29 CML 29d

[ PV#2 PV-f PV-fl PV-h ] Area 7 [ 7t VS root s ] Rostral parietal operculum Posterior parietal area Caudal parietal operculum [ 7op ] Inferior Parietal Lobule [ 7a/7b PCi ] Area 7a Caudal inferior parietal lobule [ PGc PGlat PGmed SPG ] Occipitoparietal area Area 7b Midpart of the inferior parietal lobule Rostral inferior parietal lobule Cortex of the intraparietal sulcus Lateral intraparietal area [ 7ip LIPd+LIPv POa ] Lateral intraparietal area (external part) [ LIPd POa-e ] Lateral intraparietal area (internal part) [ LIPv POa-i ] Ventral intraparietal area [ IPd VIPl VIPm ] Posterior intraparietal area Anterior intraparietal area Medial intraparietal area [ 5ip PEa PEip ] Dorsal parietal cortex (= SPL and precuneus) Superior Parietal Lobule [ 2/5 5D 5V 5m ] Rostral superior parietal lobule [ PE#1 PE#2 ] Receptive field for the foot in Area5 Caudal and medial superior parietal lobule [ 5b PEc#2 PEp ] Medial parietal cortex (= Precuneus) Parietal area PG, medial part [ 7m#1 MDP ] Area 31 Parietal area PE (cingulate part) [ SSA ] Cingulate Gyrus according to GM-Definition Anterior cingulate area 24 [ LA#1 ] Area 24c (rostral part of the cingulate sulcus) [ 24c-arm 24c-d 24c-l 24c-m 24c-v M3 ] Area 24d (rostral part of the cingulate sulcus) [ 24d-arm 24d-leg CMAr ] Area 24b Area 24a Area 23 [ CGp LC#1 ] Area 23c [ 23c-d 23c-l 23c-m 23c-v 6c CMAc CMAd#1 ] [ CMAv M4 ] Area 23b Transitional sensory area Area 23a Area 26 [ RSpC Rsp rspl-c ] Area 29 Caudomedial lobule Area 29d

Ring Number

Degree

Number of times studied

Number of Connections reported

6

63

17

133

10 9 11

9 3 13

6 3 10

20 3 15

7

68

7

101

8 10

52 77

29 28

74 104

9 8 11 10 7 8

38 92 38 54 0 128

10 29 8 13 2 33

46 143 47 73 0 207

9

15

10

19

11

18

11

21

10

43

34

64

9 11 10

17 14 50

7 9 23

21 20 83

7 8

0 46

2 37

0 100

9

57

14

87

11 10

4 58

1 11

4 82

8 9

0 107

2 17

0 149

11 10

54 61

11 9

64 72

6 8

0 176

2 55

0 383

9

77

28

135

11

27

23

48

10 9 8

67 47 82

16 15 37

100 76 169

11

88

43

198

10 9 11 7

33 25 19 5

9 1 9 12

55 29 31 6

8 10 9

15 2 9

14 1 9

20 2 12

continued on next page...

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...continued from previous page

Level

Acronym

Full Name [Merged Brain Regions]

5

29a-c

4

30

3

25

2

Insula

3

Ig#1

3

Ri#1

3

IPro

3

Pi#1

3 4

IA#1 Idg

4

Ia#2

5

Ial

5

Iam

5 5

Iapm Iai

2 3 4

TL#2 TCv TF

5

TFM

5

TFL

4

Per#1

5

35

5

36

6

36c

6

36r

6 7

TG TPPro

8

TPag

8 8

TPg TPproD

9 9 7 3

TPdgv TPdgd 36p PHC

4

ENT

5

EL

[ 29m ] Cortical area 29a-c [ 29a 29b 29c 29l ] Retrosplenial area 30 [ 30d 30pv ] Area 25 [ 14c FL ] Insula [ I#3 I#3m INS PI#2 ] Granular insular cortex [ GI Ip#3 ] Retroinsular area [ reIpt reIt ] Insular proisocortex [ IP#2 ] Parainsular field/cortex [ paI#1 ] Anterior insula Dysgranular insular cortex [ DI#2 Id ] Agranular insula [ AI#2 Ia-p Iac Iag ] Lateral agranular insular cortex [ Iapl ] Medial agranular insular cortex [ Iav ] Posteromedial agranular insular cortex Intermediate agranula insular cortex [ Iad ] Temporal Lobe according to GM-Definition Ventral Temporal Cortex Temporal area TF [ TFO VTF ] Temporal area TF (medial part) [ TF2 ] Temporal area TF (lateral part) [ TF1 ] Perirhinal cortex [ Peri Pr#2 ] Area 35 [ 35-I 35-II 35-III 35-IV 35-V 35-VI 35a ] Area 36 [ 36-I 36-II 36-III 36-IV 36-V 36-VI 36/TF/TE ] Caudal part of area 36 [ 36cl TLO TLc ] Rostral part of area 36 [ 36rm TLR ] Temporopolar area TG Temporal proisocortex [ 36d Pro#1 TempPro ] Agranular area of temporal polar cortex [ TPa-p ] Granular area of temporal polar cortex Dysgranular Temporopolar Cortex [ DLP DMP TPdg ] Ventral dysgranular area of temporal polar cortex Dorsal dysgranular area of temporal polar cortex Cortical area 36p [ 36pl 36pm ] Parahippocampal cortex [ PH paraHC ] Entorhinal cortex [ 28 28-I 28-II 28-III 28-V 28-VI 28-iv E EC#1 ER#2 ] Lateral field of entorhinal cortex [ 28L 28b Pr#1 ]

Ring Number

Degree

Number of times studied

Number of Connections reported

11

20

20

50

10

20

17

30

9

82

44

142

6

52

5

66

11

48

26

86

10

22

24

44

9

3

2

3

11

34

16

40

7 10

0 58

4 20

0 76

8

37

16

47

9

23

5

42

11

49

5

67

10 9

51 86

2 3

61 120

2 3 8

0 0 127

1 2 54

0 0 199

11

35

7

40

10

43

7

47

4

12

4

12

9

74

57

136

5

95

42

176

11

53

22

68

10

83

19

130

6 7

96 49

18 23

134 71

9

17

4

25

11 8

24 15

3 5

34 23

10 9 11

10 10 14

2 2 4

13 13 19

6

8

4

13

7

92

61

176

8

27

20

32

continued on next page...

46

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...continued from previous page

Level

Acronym

6

ELr

6

ELc

5

EI

5 5

ER#1 28m

5 5 5 4

EO ECL EC#2 S#1

5 5 4

Su#2 Sb Pros.

4

PaS

4

TH

4

PrS

3

Hip

4

CA1

4

DG

4

CA3

3 4 5

STG STP#2 A1

5 5

STPg A2

6

Pa#2

7

ProK

7

paAc

6

paAlt

7

L#1

7

CL#4

7 4

AL#4 TA

5 6

Ts

6 6 5 3

ST2 ST1 Tpt

4

ST3

TE 20

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

Lateral field (rostral part) of entorhinal cortex [ Pr1 ] Lateral field (caudal part) of entorhinal cortex [ 28S-I 28S-III 28S-V 28s ] Intermediate field of entorhinal cortex [ 28I-III 28i ] Rostral field of entorhinal cortex medial entorhinal cortex [ 28M-III 28a ] Olfactory field of entorhinal cortex Caudal limiting field of entorhinal cortex Caudal field of entorhinal cortex Subiculum [ S-SM S-SP Sub Subr ] Subiculum, uncal portion Subiculum, body portion prosubiculum [ PoS ProS#2 ProS-SM ProS-SP ] Parasubiculum [ ParaS ] Temporal area TH [ THO THc THr ] Presubiculum [ 27 PreS PreS-Lpe Psb Psub ] Hippocampus [ CA2 CA2-SLM CA4 H#1 HF h#3 ] CA1 subfield of Ammon‘s horn [ CA1-SLM CA1-SM CA1-SP CA1-SR CA1a CA1med-sm ] [ CA1med-sp CA1med-sr CA1t’ CA1t’-SP ] dentate gyrus [ DG-gc DG-ml ] CA3 subfield of Ammons horn [ CA3-SLM ] superior temporal gyrus [ 22 STGf STGi STGm STGo ] Supratemporal plane Primary auditory cortex [ KA R#2 RA RP paAr ] Supratemporal cortex, granular Secondary auditory cortex [ AII belt ] Postauditory field [ CM#1 P-m RTM ] auditory prokoniocortex [ A-m RM proA ] Caudal auditory parakoniocortex [ CP ] Lateral auditory parakoniocortex [ RTL lateral-belt ] Lateral auditory field [ LA#2 ML#1 PL#5 ] cudal lateral auditory (belt) [ Toc#2 ] anterior lateral auditory belt Temporal area TA [ STGa STGp#1 ] Area temporalis superior Superior temporal area 3 [ 3#3 4#3 STGl STGr Ts3 ] Superior temporal area 2 Superior temporal area 1 Temporoparietal cortex Inferotemporal area TE [ IT TEO+TE TEO+TE+TE3 tmps ] Area 20

10

21

13

Number of Connections reported 23

9

10

14

17

11

37

18

49

10 9

26 15

6 12

30 22

11 10 9 8

17 21 44 32

6 6 6 38

18 28 62 46

11 10 9

5 5 26

1 1 34

6 6 34

11

22

24

23

10

110

48

158

9

39

38

46

8

24

66

39

11

45

87

116

10

10

31

17

9

12

44

15

5

29

10

61

6 11

0 49

1 40

0 109

10 7

24 33

1 9

24 40

8

11

12

22

9

19

11

32

11

28

6

42

8

40

17

91

10

33

7

54

9

23

5

32

11 7

21 28

3 13

27 49

8 10

0 57

2 20

0 76

9 11 10 6

50 39 50 115

16 16 16 45

65 47 61 222

7

19

9

28

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...continued from previous page

Level

Acronym

Full Name [Merged Brain Regions]

5

AITv

5

CIT

6

CITd

6

CITv

4

21

5

AITd

6

TEa#3

6 5

TEm PIT

6

PITd

6

PITv

3

STS

4 5 6

STSd TPO TPOc

6 6

TPOi TPOr

5 4 5 5 4 5 5 5 5

TAa STSf PGa IPa OAa MT MTp FST MST

6 6 2 3 4 5 5 6 6 5

MSTp MSTd OC#2 VAC OA V3A V3 V3d V3v V4

6

V4t

6

V4d

7 7 6 5

DLr DLc V4v VPP

[ ITi TE1-3 TEv ] Anterior inferotemporal area (ventral) [ TE1#1 TE1#2 TEav ] Central inferotemporal area [ TEpv ] Central inferotemporal area (dorsal) [ TE3#1 ] Central inferotemporal area (ventral) [ TE2#1 TE2#2 ] Area 21 [ ITm ] Anterior inferotemporal area (dorsal) [ STSv TEa/m TEad TEm/TEa ] anterior part of area TE [ TEa#1 TEa#2 ] Cortical area TEm Posterior inferotemporal area [ TEO TEO+ TEp TEpd ] Posterior inferotemporal area (dorsal) [ TEOd ] Posterior inferotemporal area (ventral) [ TEOv ] Superior temporal sulcus [ ST STP#1 ] Superior temporal sulcus, dorsal Temporal parietooccipital associated area in the STS Temporoparietal asscociated area (caudal part) [ STPp TPO3 TPO4 ] Temporoparietal associated area (intermediate part) Temporoparietal associated area (rostral part) [ STPa TPO1 TPO2 ] Temporal area TAa Superior temporal sulcus, fundus Cortical area PGa Intraparietal sulcus associated area in the STS Cortical area OAa Middle temporal area [ V5 V5a ] Peripheral part of area MT Floor of superior temporal sulcus Medial superior temporal area [ DMZ MSTm ] Medial superior temporal area (posterior) Medial superior temporal area (dorsal) [ MSTc MSTda MSTdp ] OccipitalLobe according to GM-Definition Visual anterior cortex Extrastriate area OA [ 19 ] Visual area 3A Visual area 3 [ region-2 ] Dorsal visual area 3 Ventral visual area 3 [ VP#1 ] Visual area 4 [ region-3 region-4 region-6 region-7 ] V4 transitional area [ V4ta V4tp region-5 ] Visual area 4 (dorsal part) [ DL#1 ] dorsolateral visual cortex, rostral part dorsolateral visual cortex, caudal part Visual area 4 (ventral part) Ventral posterior parietal area

Ring Number

Degree

Number of times studied

Number of Connections reported

9

68

19

102

8

29

7

38

11

11

14

13

10

36

13

39

7

12

9

14

8

57

11

80

9

30

18

34

11 8

14 112

15 47

18 216

10

18

8

25

9

20

4

20

6

54

7

117

7 8 11

25 72 51

2 15 14

28 98 67

10 9

6 30

2 12

6 46

11 8 10 9 7 11

45 0 36 37 15 75

12 1 13 17 7 52

58 0 48 47 21 113

10 9 8

8 48 22

7 23 36

8 73 27

11 10

20 49

3 6

20 70

4 5 6

0 0 38

5 2 27

0 0 71

9 8

32 35

24 29

47 46

11 10

8 38

14 27

12 68

7

78

50

138

9

26

24

35

8

18

7

23

11 10 9 11

2 2 6 2

2 2 6 2

4 4 8 3

continued on next page...

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...continued from previous page

Level

Acronym

5 5

DI#1 PO#4

6 6

V6A V6

5

DP

4 3

VOT V1

3

ProSt

3

V2

1 2

BG Amyg

3

B#2

4

Bla

4

Abpc

4 4

Bi ABd

4 4 4

Bvl ABv MB

4

ABvm

4

ABmg

3

A

3 3

I#2 ME#1

3

CE#1

3

PAC#1

4

AHA

4

PAC2

4

Co

5 5 5 3 4 5 5 4 4 2

COp NLOT COa L#2 Ldm Ldi Ld#2 Lv Lvl SN

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

dorsointermediate visual field medial visual association area [ M#3 PO#1 ] Visual area V6A Visual area 6 [ DM#1 ] Dorsal prelunate gyrus [ DPL ] Ventral occipitotemporal area Visual area 1 [ 17 17 I LVQ OC StriateC StriateC-I StriateC-II StriateC-III ] [ StriateC-IV UVQ V1 I V1 II V1 III ] Prostriate cortex [ P#4 PRO ] Visual area 2 [ 18 OB V2 clf V2 ilf V2 iuf V2 puf V2d V2v ] [ region-1 v2(+) v2(-) v2(0) ] Basal Ganglia according to GM-Definition Amygdala [ amg ] basal amygdaloid nucleus [ AB#2 ABa ACC-B Amyg AB B#4 BA ] Basolateral nucleus of amygdala [ ABl BL#2 Bl#1 LB ] Accessory basal amygdaloid nucleus, parvicellular part [ BAp BLp Bp Bpc Bpl PL#2 PL#4 ] [ PLl PLm ] Basal amygdaloid nucleus, intermediate part Accessory basal amygdaloid nucleus, dorsal division [ Bd ] Basal amygdaloid nucleus, ventral lateral division Accessory basal amygdaloid nucleus, ventral division Medial basal nucleus of the amygdala [ ABm BM#3 Bm#1 ] Accessor basal nucleus (amygdala), ventromedial division [ Abs Bvm ] accessory basal nucleus (amygdala), magnocellular subdivision [ BAm#1 BLm Bmc Bmg abmc ] anterior amygdaloid area [ AA AAA ] Intercalated amygdaloid nucleus Medial nucleus of the amygdala [ M#1 ] central nucleus of the amygdala [ C#2 CEl CEm#1 CEmc Cec Cl#3 Cm#3 ] periamygdaloid cortex [ APir PACo PACo#1 VCo VCoIf VCoIt VCoS ] amygdalohippocampal area [ AHAd AHAv HATA ] Periamygdaloid cortex 2 [ BPACs CTA PAC1 PAC3 PACs pam#1 ] cortical nucleus (amygdala) [ Amyg CO CN ] cortical nucleus, posterior division Nucleus of the lateral olfactory tract cortical nucleus, anterior division lateral nucleus, amygdala [ Amyg L LAT LT ] Lateral amygdaloid nucleus, dorsomedial region Lateral nucleus (amygdala), dorsal intermediate division Lateral nucleus (amygdala), dorsal division Lateral nucleus (amygdala), ventral division lateral nucleus (amygdala), ventrolateral subdivision substantia nigra [ SN.com SN.ret ]

10 8

2 35

2 21

Number of Connections reported 4 48

9 11

33 41

6 10

48 57

10

36

16

40

9 11

7 47

3 113

9 158

10

3

3

3

9

82

68

205

5 6

0 23

1 17

0 49

8

65

56

91

11

53

27

68

10

45

49

81

9 11

43 23

10 2

50 45

10 9 11

19 23 38

1 1 25

27 32 46

10

30

10

51

9

49

32

82

11

24

30

26

10 9

6 25

13 38

6 31

11

26

61

50

7

25

26

36

10

16

43

21

9

21

44

52

8

10

21

13

11 10 9 7

12 9 14 86

14 13 16 40

14 9 15 134

8 11 10 9 11 10

0 58 35 52 43 8

2 4 4 4 7 6

0 69 43 68 50 8

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...continued from previous page

Level

Acronym

2

SI#2

2

Sub.Th

2

GPe

2 3

STR Cd

4

Cd t

4

Cd g

3

Pu

4

Pu r

4

Pu c

2

Clau

1

MB#2

1

OFC

Full Name [Merged Brain Regions]

Ring Number

Degree

Number of times studied

substantia innominata [ Acc#1 Acc-core Ch1 Ch2 Ch3 Ch4 Ch4al Ch4am ] [ Ch4id Ch4iv Ch4p MS NBM NVDB VP#3 ] Nucleus subthalamic [ ZI Zic ] Globus pallidus, external part [ GPi ] striatum Nucleus caudatus [ Cd b Cd b i c Cd b i d Cd b i v Cd b l c Cd b l d ] [ Cd b l v Cd b m c Cd b m d Cd b m v Cd h Cd h i c Cd h i d ] [ Cd h i v Cd h l c Cd h l d Cd h l v Cd h m c Cd h m d Cd h m v ] Nucleus caudatus; tail [ Cd t i c Cd t i d Cd t i v Cd t l c Cd t l d Cd t l v Cd t m c ] [ Cd t m d Cd t m v ] Nucleus caudatus; genu [ Cd g i c Cd g i d Cd g i v Cd g l c Cd g l d Cd g l v Cd g m c ] [ Cd g m d Cd g m v ] Putamen [ Pu m i c Pu m i d Pu m i v Pu m l c Pu m l d Pu m l v Pu m m c ] [ Pu m m d Pu m m v ] Putamen; rostral [ Pu r i c Pu r i d Pu r i v Pu r l c Pu r l d Pu r l v Pu r m c ] [ Pu r m d Pu r m v ] Putamen; caudal [ Pu c i c Pu c i d Pu c i v Pu c l c Pu c l d Pu c l v Pu c m c ] [ Pu c m d Pu c m v ] Claustrum [ CL#1 ] Mid Brain [ APT CG DLT GPO NCS NOT NPA NPC ON ] [ PG#2 PPN#1 PPN#2 PPT#2 RTP SC SC I SC III SC II 1 SC II 2 ] [ SC II 3 SC IV SC V SC VI SC VII SL SZ Teg.a VLZ VTA ] Olfactory Complex [ AON B-Olf OLF OT PC#2 POC Pir ]

9

55

19

Number of Connections reported 194

11

3

6

3

10

4

6

7

7 8

0 52

1 123

0 237

9

17

44

56

11

28

57

87

8

20

46

43

10

46

50

122

9

27

49

72

11

25

17

26

10

20

81

99

9

17

35

26

The color of each row is derived from corresponding color in Figure S6.

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Table S2: A summary of number of connections in major brain pathways DiE BG Cx

DiE 10 37 505

BG 10 186 446

Cx 953 289 4129

Diencephalon (DiE), basal ganglia (BG), and cortex (Cx). The (i, j)-th entry shows number of connections from row i to column j, for example, there are 289 edges from BG to Cx and 446 edges from Cx to BG. There are 953 feedforward connections from thalamus to cortex, and 505 feedback connections from cortex to thalamus, thus reciprocity in these relays is only of the order of 34% as compared to 42% for the entire graph. We found 248 short loops of length 2 (thalamus to cortex and back) involving 55 thalamic regions and 60 cortical regions thus confirming the pervasiveness of short thalamocortical loops [25, 18].

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Table S3: A summary of number of connections in major corticocortical pathways DiE BG OC#2 Pl#6 TL#2 FL#2 CgG#2 Insula Num Areas Avg InDegree Avg OutDegree

DiE 10 37 61 103 92 197 37 15 75 8.50

BG 10 186 16 47 172 145 22 44 41 15.83

OC#2 37 8 77 38 60 12 0 0 23 11.09

Pl#6 160 8 53 178 99 178 48 41 41 20.67

TL#2 105 140 77 83 684 238 63 78 88 17.67

FL#2 600 95 46 251 388 695 202 101 81 30.16

CgG#2 25 14 6 55 70 151 39 13 18 21.94

Insula 26 24 0 21 28 32 10 14 12 14.27

14.16

14.25

15.85

20.45

19.16

20.71

24.64

27.45

Diencephalon (DiE), basal ganglia (BG), and six cortical constituents: temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2). The (i, j)-th entry shows number of connections from brain substructure in row i to brain substructure in column j. For each brain substructure, we show the number of its sub-regions (Num Areas), average in-degrees (the ratio of the total number of connections entering the substructure to the number of regions in it), and average out-degrees (the ratio of the total number of connections leaving the substructure to the number of regions in it). incoming links) and average out-degrees (defined as the average number of outgoing links) and number of cortical areas in each column.

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Table S4: Brain regions associated with each fiber system are listed in the corresponding row Fiber System Felleman-Van Essen [8] Dorsal Ventral [17]

Arcuate Fasciculus [19] Cingulum Bundle [19] Extreme Capsule [19] Fronto-Occipital Fasciculus [19] Inferior Longitudinal Fasciculus [19] Middle Longitudinal Fasciculus [19] Superior Longitudinal Fasciculus [19] Uncinate Fasciculus [19]

53

Brain Regions V1 V2 V3 V3v V3A V4 VOT V4t MT FST PITd PITv CITd CITv AITd AITv TPOc TPOr TF TH MSTd MSTp PO#4 PIP#1 LIP VIP MIP PGm DP 7a FEF 46 V2 ProSt V1 STS TE VOT OA OAa TH TF MIP AIP PIP#1 VIP LIP IPL DP PO#4 V4 V3 MST FST MTp MT IPa PGa TPO PIT AITv 36 TFL TFM PECg 31 PGm PEc#1 PEm LIPi LIPe 7a V6 V6A V4v V4d V4t V3v V3d V3A MSTd MSTp PITv PITd TEm CITv CITd Opt PG#1 TPO Tpt F2 F7 TPOr TPOc 8Ad 9/46d 25 PrS TH ENT TF 30 29 6M 6D 32 EC#2 ECL EO 28m ER#1 EI EL 36 35 TFL TFM 29a-c 29d 7a F6 F3 F2 F7 9 11 14 ELc ELr TG 36r 36c Opt PG#1 SMAc SMAr 46d D9 M9 L9 11m 11l 14r 14O 36p TPPro 8Ad 9/46d TPproD TPg TPag TPdgd Insula Pi#1 Ri#1 Ig#1 24 TH Ia#2 Idg 24a 24b 24c 32 IPa TAa TPO 36 Iai Iapm Iam Ial TPOr TPOi TPOc ST2 ST3 paAlt TG 36r 36c 45 47/12 AL#4 CL#4 L#1 36p TPPro 8Ad 45B 45A 9/46d TPproD TPg TPag TPdgd TPdgv 6D DP PO#4 PGm 7a F2 F7 8B 9 V6 V6A Opt PG#1 46d D9 M9 L9 8Ad V2 V1 20 TH TF LIP DP V4 V3 MST FST MT IPa PIT CIT AITv 36 TFL TFM LIPi LIPe V4v V4d V4t V3v V3d V3A MSTd MSTp PITv PITd TEa#3 CITv CITd TG 36r 36c Opt DLc DLr 36p TPPro TPproD TPg TPag 23 TF 30 23a TSA 23b 23c DP IPa PGa TAa TPO Tpt A1 TFL 7a TPOr TPOi TPOc paAlt Pa#2 Opt PG#1 AL#4 CL#4 L#1 paAc ProK LIP PFop 6M 6D 44 6V 31 PGm PEc#1 PEm LIPi LIPe 7b 7a F6 F3 F2 F7 F4 6Va 6Vb 4c PrCO F5 46 9 PF#1 PFG#1 Opt PG#1 SMAc SMAr 46dr 46vr 46f PS 46d 46v D9 M9 L9 8Ad 9/46d 9/46v Amyg L#2 PAC#1 CE#1 ME#1 I#2 A B#2 25 24 Lvl Lv Co PAC2 AHA ABmg ABvm MB ABv Bvl ABd Bi Abpc Bla TH ENT Per#1 TF 24a 24b 24c 32 Ld#2 Ldi COa NLOT COp IPa AITv EC#2 ECL EO 28m ER#1 EI EL 36 35 TFL TFM 11 10 13 14 TEa#3 ST1 ELc ELr TG 36r 36c 11m 11l 47/12 10o 10d 10v 10m 13a 13M 13L 14r 14O 36p TPPro TPproD TPg TPag TPdgd TPdgv

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Table S5: A core decomposition of the brain network into shells and finer subshells Shell S0

Fine Shell F0,1

S1 S2

F1,1 F2,1

S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

F3,1 F4,1 F5,1 F6,1 F7,1 F8,1 F9,1 F10,1 F11,1 F12,1 F13,1 F14,1 F15,1 F15,2 F16,1 F16,2 F17,1 F17,2 F18,1 F18,2 F19,1 F19,2 F20,1 F20,2 F21,1 F21,2 F22,1 F22,2 F23,1 F23,2 F24,1 F24,2 F25,1 F25,2 F26,1 F26,2 F26,3 F26,4 F27,1 F27,2 F28,1 F28,2 F28,3 F28,4 F28,5 F29,1 F29,2 F29,3 F29,4 F29,5 F29,6 F29,7 F29,8 F29,9 F29,10

S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26

S27 S28

S29

Brain Regions Br BG Cx DiE STR CgG#2 FL#2 OC#2 Pl#6 TL#2 Pfc IA#1 VAC PCd#2 PCip TCv GN Ldm PCm STP#2 STSf Ts 9/46 Tha VP#2 PN 4a 4b 6b-beta CMA#2 CML OFO DI#1 VPP PIl-s PLa#1 SMAc 46f DLc DLr Sub.Th IPro ProSt MI#1 PP 10d GPe C#4 5 Foot PIp 46dr 26 SII-f AD#1 MDcd Sb Su#2 PLvm PLvl PLd Cs#2 14O 46vr I#2 44 MDl M2-FL V4v TPOi 8Ac VN VOT AV PT#2 M2-HL Cim PIm PMm VAdc VPS 10v L9 SN PHC AN OFap MTp PMl V3d PFop NLOT 29d PIc PIl Co PFCorb DG LGN MDpm ELc TPdgd TPdgv Cif Clc CITd Pa#2 ML CA3 21 Per#1 COp VPI 45B 9/46v belt s PGop PAa 28m 36p MB#2 IL#2 PC#1 AIP LD#1 COa TEm Cd t 29 OAa LIPe TPproD PITd TPag OFC Bvl AHA EO ABd ABv PR#4 PIP#1 4c MDmf Cdc V4d PITv Amyg PAC2 VL LIPi ELr MI-body 20 Pu 23a PaS ECL VPM VPLo ProK Hip Gu A belt sm ABvm 30 29a-c 6Vb VLps 47/12 MSTp ME#1 3#1 AM#1 MDdc MG Ial EL MDfi VApc 10m AL#4 ProM#2 CE#1 Ri#1 S#1 STPg MST TPg Cd g TSA MI-of TA Pros. Re PI#3 6Va CIT ER#1 V4t CL#4 Hyp STG 3b paAc Clau PAC#1 Pu c 24d M1-HL VLm 45A 8Ad 9/46d D9 V1 Ret STSd OA V3v V3A V6 CITv TEa#3 paAlt VPLc L#1 MB SG PO#4 3a DP V3 Csl S1 FD#1 X PFG#1 Opt 23b TPOr 1#1 A2 TFM FST IPa VLc V6A Insula Pi#1 VIP EI MSTd CA1 Pf#2 Ld#2 MT PGa V2 EC#2 TFL Pul#1 SPL PrS SMAr Pul.o F4 VLo PF#1 Ia#2 PL#3 PrCO 2#1 Lvl Lv MIP V4 A1 36c Bi CM#2 Ldi TAa 46d Ig#1 Abpc 8 FEF Iam Iapm PEc#1 Tpt ST1 7#1 ABmg MDmc VA MDpc VPL 13M 12r ST2 ST3 TPOc TPPro 6#1 Bla Cl#2 F6 F3 PEm PECg M9 12m 11l PG#1 SI#2 Cd M1 S2 STS Pu r M1-FL IPL Pcn Li F2 7a 31 AITv AITd VAmc 13L 10o continued on next page...

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continued on next page...

Shell

Fine Shell F29,11 F29,12 F29,13 F29,14

Brain Regions 6D 6V F5 PIT 35 TPO 14r 11m 46v 36r B#2 L#2 24a 24b Idg PM#3 Iai 7b 45 8A PS 25 TE 24c 23c 6M LIP ENT TH TF F7 13 12 PGm 36 13a 12l TG 24 23 MD 32 8B 14 10 9 11 46 12o end of table

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Table S6: Number of connections to be added or deleted in order to affect the core Number of Connections to Core 129 111 98 90 87 82 80 78 77 75 73 72 70 69 64 63 61 60 59 57 56 55 54 53 52 51 50 48 47 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16

Number of Extra Connections to Core 100 82 69 61 58 53 51 49 48 46 44 43 41 40 35 34 32 31 30 28 27 26 25 24 23 22 21 19 18 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13

Brain Regions 46 24 32 12o 9 12l F7 11 MD 13a TE PGm TH TF 14 13 10 6M LIP 12 25 23 36 24c PM#3 8B 23c 45 24b M1 ENT 7b TPO TG 6V F2 8A 46v L#2 F5 Iai 35 M1-FL 6D Idg 36r PIT S2 14r PS Cd 6#1 SI#2 B#2 STS 24a F3 PEm PECg IPL 7#1 Pu r Cl#2 Pcn F6 AITd 12m PG#1 31 AITv VPL 13L 11m ABmg PEc#1 TPPro Ig#1 Li Ldi 7a ST2 MIP VAmc 10o M9 Bla 2#1 MDpc ST3 Abpc 8 FEF V4 Tpt 13M 11l PF#1 TPOc Bi MDmc CM#2 VA PrCO 12r 46d ST1 Lv PL#3 Pul.o Iam Iapm TAa Lvl Ia#2 F4 A1 VLo 36c Pul#1 SPL PrS SMAr V2 Pf#2 Ld#2 TFL PGa VLc 1#1 EC#2 Insula S1 23b X EI IPa CA1 A2 V6A PFG#1 TPOr L#1 PAC#1 FD#1 Csl D9 Pi#1 MB SG 6Va 3a TFM MT VLm 24d STSd CL#4 CE#1 Ret M1-HL OA VIP TA Re FST 10m CITv paAlt MSTd TPg Clau ME#1 Pu c MI-of AM#1 MDdc 6Vb Ial ER#1 MDfi TEa#3 9/46d Hyp A TSA DP VApc VLps ProM#2 VPLc AL#4 STG S#1 CIT Opt 8Ad Pu 3#1 Pros. 29a-c PO#4 3b VPLo paAc 30 23a STPg continued on next page...

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Number of Connections to Core 15 14 13 12 11 10 9 8 7 6 5

Number of Extra Connections to Core -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24

4 3 2 1 0

-25 -26 -27 -28 -29

Brain Regions PAC2 Cd g MI-body MG V3 ECL EL EO MST MDmf Cdc Gu 47/12 V6 OFC Ri#1 AHA 29 PaS V3v Amyg belt sm IL#2 ABvm VL 4c TPag PR#4 ML AIP ELr 45A V1 Hip Cd t PGop PC#1 20 Clc VPM ProK 21 OAa PAa PI#3 COa MDpm Cif V3A TEm 45B TPdgd TPdgv MB#2 Co PFCorb Per#1 LD#1 LIPe LIPi VPI COp V4t CITd PITv 36p belt s AN VN PFop NLOT OFap MTp 10v L9 V3d V4d TPproD CA3 AV MDl PT#2 29d M2-FL Cim PMl 9/46v SN 26 PHC ABd ABv AD#1 MDcd M2-HL 28m Sb Su#2 PMm Cs#2 14O 46vr PITd Pa#2 ELc MSTp 8Ac Bvl PIP#1 C#4 LGN 5 Foot PLd VPS 46dr TPOi MI#1 44 PP DG 10d Sub.Th I#2 ProSt PN 4a 4b 6b-beta CML OFO PIc VAdc SMAc 46f V4v GPe Tha IPro VOT CMA#2 SII-f VP#2 PIl PIm PIp PLvm PLvl Br BG Cx DiE STR CgG#2 FL#2 OC#2 Pl#6 TL#2 Pfc IA#1 VAC PCd#2 PCip TCv GN Ldm PCm STP#2 STSf DI#1 VPP Ts PIl-s PLa#1 9/46 DLc DLr

The third column lists a group of brain regions. All these brain regions have the same number of connections to brain regions in the innermost core. This number is shown in the first column. The 122 brain regions in the innermost core are color coded. For the brain regions in the innermost core, the second column shows how many connections can be safely deleted without removing the associated brain region from the innermost core. For the remaining brain regions, the second column shows how many connections need to be added between a brain region and the innermost core for the brain region to become a member of the innermost core. These are shown as negative numbers.

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Supporting Information

Jul 13, 2010 - macaque brain consists of 95 vertices and 2,402 edges [1], where the network models brain regions as vertices and the presence of long dis-.

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