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Graph analysis of cortical networks reveals complex anatomical communication substrate
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Image of FIG. 1.
FIG. 1.

Weighted adjacency matrix of the corticocortical connectivity of the cat comprising of 826 directed connections between 53 cortical areas (Refs. 6 and 7). The connections are classified as weak (open circles), intermediate (blue stars), and dense (red filled circles) according to the axonal densities in the projections between two areas. For visualization purposes, the nonexisting connections (0) have been replaced by dots. The network has clustered organization, reflecting four functional subdivisions: visual, auditory, somatosensory motor, and frontolimbic.

Image of FIG. 2.
FIG. 2.

Small-world properties of WS networks of equivalent size and link density as the cortical network of the cat. (a) As in Ref. 11, and are displayed normalized by the values of the initial regular lattice and . (b) and are rescaled to display the complexity of the networks such that only if (regular lattice) and only if (random graph). At (dashed line) the difference between the rescaled and is maximal.

Image of FIG. 3.
FIG. 3.

Classification of the cat cortical network and comparison to ensembles of random null models and generic models. (a) Small-world diagram displaying the rescaled clustering and pathlength of the different networks: cat cortex (●), random graphs (▲), rewired (◆), SF (▼), and WS networks (◼). (b) Cumulative degree distribution of the cat cortical network and of the random models. Error bars are very small in both figures, and hence not shown.

Image of FIG. 4.
FIG. 4.

(a) Distance matrix of the corticocortical network of the cat. Cortical areas separated by distance (dark blue), (light blue), (yellow), or (red). (b) Path multiplicity matrix representing the number of distinct shortest paths (of length ) from area to area . On average, there exist 5.2 alternative paths between every pair of areas.

Image of FIG. 5.
FIG. 5.

Number of pairs of cortical areas at distance . (a) All cortical areas considered, (b) only distance between areas in the same community, and (c) only distance between areas in different communities.

Image of FIG. 6.
FIG. 6.

Analysis of the path multiplicity. (a) Total number of shortest paths between cortical areas at distance . (b) Average number of shortest paths between areas at distance . [(c) and (d)] Probability that a pair of nodes at distance is connected by shortest paths.


Generic image for table
Table I.

Average clustering and shortest pathlength of the cat cortical network and equivalent random network models of the same size and link density . “Rewired” additionally conserves the same input and output degree sequence. Values are the average over 100 realizations.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Graph analysis of cortical networks reveals complex anatomical communication substrate