Analytical solution of the voter model on uncorrelated networks

By Federico Vazquez, Víctor M. Eguíluz. 2008

166 citations recorded by the source corpus.

We present a mathematical description of the voter model dynamics on uncorrelated networks. When the average degree of the graph is μ⩽2 the system reaches complete order exponentially fast. For μ>2, a finite system falls, before it fully orders, in a quasi-stationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to , while an infinitely large system stays ad infinitum in a partially ordered stationary active state. The mean lifetime of the quasi-stationary state is proportional to the mean time to reach the fully ordered state T, which scales as , where N is the number of nodes of the network, and μ2 is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0f0aa633043c9b3c85ec605cf7d870e540c58edd

Citations in the corpus

• Binary-state dynamics on complex networks: pair approximation and beyond (2012, unknown): “ation (PA) theories improve upon the accuracy of MF theories—at the cost of extra complexity in the resulting system of differential equations—by including dynamical correlations 2 at a pairwise level [36, 37, 38, 39, 40, 41, 42, 43]. In addition to the fraction of active nodes in each degree class (”