^{1,a)}, Changsong Zhou

^{2}and Jürgen Kurths

^{3}

### Abstract

Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (*i*) a large density of connections, (*ii*) segregation of cortical areas into clusters, and (*iii*) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other.

Traditionally, complex dynamical systems are characterized by a large number of nonlinearly interacting elements. The recent discovery of an intricate and nontrivial interaction topology among the elements in natural systems introduces a new ingredient to the spectrum of complexity. A network representation provides the system with a form (topology) which can be mathematically tractable toward uncovering its functional organization and the underlying design principles. The term

**is coined because most real systems have neither a regular nor a completely random topology but survive in some intermediate state, probably governed by rules of self-organization. For example, the axonal pathways (white matter) transmitting electrical information between regions of the cerebral cortex (gray matter) form a complex network with very particular properties.Information of different modalities (visual, auditory, etc.) entering the nervous system follows particular paths of processing, typically separated from the processing paths of other modalities. This segregation permits specialized information processing. However, achieving a coherent and comprehensive perception of the real world requires that information of all modalities are combined. Corticocortical networks of the macaque monkey and cat have been found to be organized into clusters, facilitating the segregation of areas specialized in one sensory modality. Where and how the integration happens is still unknown. In this paper, we present a statistical analysis of the corticocortical communication paths. We find that cortical processing is governed by very short paths, allowing for fast behavioral responses. Moreover, cortical areas may influence each other via different alternative paths, suggesting rich and complex information processing capabilities. Of particular interest, we find that communication between areas of different modalities is mediated by few, highly connected areas, emphasizing the central role of these hubs for the multisensory information processing and integration.**

*complex*We thank the constructive comments of two anonymous referees. G.Z.-L. and J.K. are supported by the Deutsche Forschungsgemeinschaft (Grant Nos. EN471/2-1, KL955/6-1, and KL955/14-1). C.S.Z. is supported by the Hong Kong Baptist University.

I. INTRODUCTION

A. Corticocortical connectivity of the cat

II. CLASSIFICATION OF CORTICAL NETWORKS

A. Optimal in the Watts–Strogatz model

B. Comparison to random graph models

III. CORTICAL COMMUNICATION PATHS

A. Multiple and alternative communication paths

IV. CONCLUSIONS AND DISCUSSION

### Key Topics

- Networks
- 40.0
- Information processing
- 22.0
- Cluster analysis
- 9.0
- Nervous system
- 8.0
- Information integration
- 7.0

## Figures

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.

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.

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.

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.

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.

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.

(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.

(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.

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.

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.

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.

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.

## Tables

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.

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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