The small world coefficient 4.8 \xb1 1 optimizes information processing in 2D neuronal networks

Abstract

Small world networks have recently attracted much attention because of their unique properties. Mounting evidence suggests that communication is optimized in networks with a small world topology. However, despite the relevance of the argument, little is known about the effective enhancement of information in similar graphs. Here, we provide a quantitative estimate of the efficiency of small world networks. We used a model of the brain in which neurons are described as agents that integrate the signals from other neurons and generate an output that spreads in the system. We then used the Shannon Information Entropy to decode those signals and compute the information transported in the grid as a function of its small-world-ness ({rm{SW}}), of the length (triangle t) and frequency (f) of the originating stimulus. In numerical simulations in which {rm{SW}} was varied between 0 and 14 we found that, for certain values of triangle t and f, communication is enhanced up to 30 times compared to unstructured systems of the same size. Moreover, we found that the information processing capacity of a system steadily increases with {rm{SW}} until the value {rm{SW}}=4.8pm 1, independently on triangle t and f. After this threshold, the performance degrades with {rm{SW}} and there is no convenience in increasing indefinitely the number of active links in the system. Supported by the findings of the work and in analogy with the exergy in thermodynamics, we introduce the concept of exordic systems: a system is exordic if it is topologically biased to transmit information efficiently.