Brain networks: small-worlds, after all?
Lyle E. Muller, Alain Destexhe and Michelle Rudolph-Lilith
The New Journal of Physics 16: 105004, 2014.
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.
return to main page