Brain networks: small-worlds, after all?
Lyle Muller, Alain Destexhe and Michelle Rudolph-Lilith

New Journal of Physics 16: 105004, 2014.

Copy of the full paper (PDF)
Since its introduction, the “small-world” effect has played a central role in network science, particularly in the analysis of the complex networks of the nervous system. From the cellular level to that of interconnected cortical regions, many analyses have revealed small-world properties in the networks of the brain. In this work, we revisit the quantification of small-worldness in neural graphs. We find that neural graphs fall into the “borderline” regime of small-worldness, residing close to that of a random graph, especially when the degree sequence of the network is taken into account. We then apply recently introduced analytical expressions for clustering and distance measures, to study this borderline small-worldness regime. We derive theoretical bounds for the minimal and maximal small-worldness index for a given graph, and by semi-analytical means, study the small-worldness index itself. With this approach, we find that graphs with small-worldness equivalent to that observed in experimental data are dominated by their random component. These results provide the first thorough analysis suggesting that neural graphs may reside far away from the maximally smallworld regime.