# American Institute of Mathematical Sciences

2011, 2011(Special): 1279-1288. doi: 10.3934/proc.2011.2011.1279

## Random graph and stochastic process contributions to network dynamics

 1 Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States 2 Department of Mathematics, Ohio State University, Columbus, OH 43210, United States 3 Department of Psychology, University of Iowa, Iowa City, IA 52242, United States

Received  September 2010 Revised  July 2011 Published  October 2011

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.
Citation: Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279
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