Random walks in directed modular networks

Author(s)

Comin, Cesar H. ; Viana, Mateus P. ; Antiqueira, Lucas ; Costa, Luciano Da F.

• Document type: Journal article
• Source: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 13-pg., 2014-12-01.

Abstract

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 no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency, in modular networks. 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 the internal degree of the nodes does not play a crucial role in their efficiency, when considering the Erdos-Renyi and Barabasi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems. (AU)

• FAPESP's process: 10/16310-0 - Dynamical processes in geographical networks
• Grantee: Matheus Palhares Viana
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 11/22639-8 - Unveiling the relationship between structure and dynamics on modular networks
• Grantee: Cesar Henrique Comin
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 12/50986-7 - Graph spectra and complex network evolution
• Grantee: Luciano da Fontoura Costa
• Support Opportunities: Regular Research Grants