Polynomial Growth in Branching Processes with Diverging Reproductive Number

Alexei Vazquez
Phys. Rev. Lett. 96, 038702 – Published 27 January 2006

Abstract

We study the spreading dynamics on graphs with a power law degree distribution pkkγ, with 2<γ<3, as an example of a branching process with a diverging reproductive number. We provide evidence that the divergence of the second moment of the degree distribution carries as a consequence a qualitative change in the growth pattern, deviating from the standard exponential growth. First, the population growth is extensive, meaning that the average number of vertices reached by the spreading process becomes of the order of the graph size in a time scale that vanishes in the large graph size limit. Second, the temporal evolution is governed by a polynomial growth, with a degree determined by the characteristic distance between vertices in the graph. These results open a path to further investigation on the dynamics on networks.

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  • Received 4 May 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.038702

©2006 American Physical Society

Authors & Affiliations

Alexei Vazquez

  • Department of Physics and Center for Complex Network Research, University of Notre Dame, Notre Dame, Indiana 46556, USA

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Issue

Vol. 96, Iss. 3 — 27 January 2006

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