Convergence and divergence are mostly reciprocated properties of the connections in the network of cortical areas

Abstract

Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.

Organization of signal flow in directed networks

“…Identification of routers, sinks, sources and circulating nodes in the real-world networks was in accordance with the known functional roles of the nodes, for related previous work see [14]. Control and other loops were already investigated, [12] and classified as positive or negative depending on the nature of edges (excitatory or inhibitory) they contained.…”

“…We analysed two biological and two artificial networks: macaque visuo-tactile cortex [13,14], signal-transduction network of a CA1 neuron [12], the call graph of the Linux kernel version 2.6.12-rc2 [9], and for comparison purposes the street network of Rome [19]. Nodes and edges are defined as follows: in the macaque cortex nodes are cortical areas and edges are cortical fibres, in the signal-transduction network nodes are reactants and edges are chemical reactions, in the call graph nodes are functions and edges are function calls, in the street network the nodes are intersections between roads and edges correspond to roads or road segments.…”

“…Convergence degree was introduced in [14] for the analysis of cortical networks and was applied to some random networks [2]. We modify the measure introduced therein, in order to capture the structure of shortest paths in a more detailed way.…”

“…Possibility to go around chordless circles necessitates simultaneous quantification of signal condensing, spreading along network edges and edge circularity. Here we generalise edge convergence and divergence [14], and take into account the existence of circles in the network, treating their effects separately from the effect of branching. For that reason we refine the definition of edge convergence and introduce the overlapping set of an edge, both notions are to be defined in a precise manner later in the text.…”

“…During signal transmission, signals are being spread and condensed in the nodes, as well as along network edges. We have previously shown [13,14] that in case of cerebral cortex, using a simplified version of the convergence degree (CD), it was possible to connect structural and functional features of the network. In complex networks, signal processing characteristics are also determined by the level of network circularity (which in biology and especially neural science is known as reverberation, for obvious reasons).…”