Random graph and stochastic process contributions to network dynamics

Pages: 1279 - 1288, Issue Special, September 2011

 Abstract        Full Text (253.4K)              

Deena Schmidt - Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States (email)
Janet Best - Department of Mathematics, Ohio State University, Columbus, OH 43210, United States (email)
Mark S. Blumberg - Department of Psychology, University of Iowa, Iowa City, IA 52242, United States (email)

Abstract: A fundamental question regarding neural systems and other applications involving networks is the extent to which the network architecture may contribute to the observed dynamics. We explore this question by investigating two different processes on three different graph structures, asking to what extent the graph structure (as represented by the degree distribution) is reflected in the dynamics of the process. Our findings suggest that memoryless processes are more likely to reflect the degree distribution, whereas processes with memory can robustly give power law or other heavy-tailed distributions regardless of degree distribution.

Keywords:  stochastic process, power law, random graph, network topology
Mathematics Subject Classification:  Primary: 60G99, 05C80; Secondary: 92B20

Received: September 2010;      Revised: July 2011;      Published: October 2011.