communicability in complex networkz

1. communicability in complex networks

Many topological and dynamical properties of complex networks are
defined by assuming that most of the transport on the network flows along
the shortest paths. However, there are different scenarios in which non-
shortest paths are used to reach the network destination. Thus the
consideration of the shortest paths only does not account for the global
communicability of a complex network. Here we propose a new measure of
the communicability of a complex network, which is a broad generalization
of the concept of the shortest path. According to the new measure, most of
real-world networks display the largest communicability between the most
connected (popular) nodes of the network (assortative communicability).
There are also several networks with the disassortative communicability,
where the most “popular” nodes communicate very poorly to each other.
Using this information we classify a diverse set of real-world complex
systems into a small number of universality classes based on their structure-
dynamic correlation. In addition, the new communicability measure is able
to distinguish finer structures of networks, such as communities into which a
network is divided. A community is unambiguously defined here as a set of
nodes displaying larger communicability among them than to the rest of
nodes in the network.

The communicability is compute using the formula in this paper

http://arxiv.org/abs/0707.0756v1