Diffusion in Directed Modular Networks

Details Diffusion in Directed Modular Networks Diffusion in Directed Modular Networks

2012-02-18

arxiv.org/abs/1202.4047v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which is no longer true for directed networks. We investigate the relationship between such probability and the inward node degree in modular networks, which we call \emph{efficiency}. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that neither the internal degree nor the communities topology play a crucial role in their efficiency. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communications systems.

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