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Voorhees B, Ryder B. Simple graph models of information spread in finite populations. R Soc Open Sci. 2015;2(5):150028doi: 10.1098/rsos.150028.
Voorhees, B., & Ryder, B. (2015). Simple graph models of information spread in finite populations. Royal Society open science, 2(5), 150028. https://doi.org/10.1098/rsos.150028
Voorhees, Burton, and Ryder, Bergerud. "Simple graph models of information spread in finite populations." Royal Society open science vol. 2,5 (2015): 150028. doi: https://doi.org/10.1098/rsos.150028
Voorhees B, Ryder B. Simple graph models of information spread in finite populations. R Soc Open Sci. 2015 May 20;2(5):150028. doi: 10.1098/rsos.150028. eCollection 2015 May. PMID: 26064661; PMCID: PMC4453248.
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R Soc Open Sci. 2015 May 20;2(5):150028. doi: 10.1098/rsos.150028. eCollection 2015 May.

Simple graph models of information spread in finite populations.

Royal Society open science

Burton Voorhees, Bergerud Ryder

Affiliations

  1. Center for Science, Athabasca University , 1 University Drive , Athabasca, Alberta, Canada T9S 3A3.
  2. Department of Mathematics , University of Victoria , Victoria, British Columbia, Canada.

PMID: 26064661 PMCID: PMC4453248 DOI: 10.1098/rsos.150028

Abstract

We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call 'single-link' graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the non-zero eigenvalues of the antisymmetric part of the Laplacian and another measure is found for cycles as the value of the transition probability for which hitting times going in either direction of the cycle are equal. A generalization of circular flow graphs is used to illustrate the possibility of tuning edge weights to match pre-specified values for graph parameters; in particular, we show that generalizations of circular flows can be tuned to have fixation probabilities equal to the Moran probability for a complete graph by tuning vertex temperature profiles. Finally, single-link graphs are introduced as an example of a graph involving a bottleneck in the connection between two components and these are compared to the partial bipartite graphs.

Keywords: fixation probabilities; graph models of populations; graph parameters

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