Voter model on heterogeneous graphs.

By Vishal Sood, Sidney Redner. Physical Review Letters, 2004

606 citations recorded by the source corpus.

We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T(N) scales as Nmu(2)1/mu(2), where mu(k) is the kth moment of the degree distribution. For a power-law degree distribution n(k) approximately k(-nu), T(N) thus scales as N for nu > 3, as N/ln(N for nu = 3, as N((2nu-4)/(nu-1)) for 2 < nu < 3, as (lnN)2 for nu = 2, and as omicron(1) for nu < 2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.

Subfields: Political Science and International Relations, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/803b8d89be73886b59e5aa44395e8081002bb1ea

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Citations in the corpus

Vital nodes identification in complex networks (2016, methodology): “The method to obtain the dynamical influence is very general and can be applied in many representative dynamics [50], such as the SIR model [156], voter model [160], Ising model [161], Kuramoto model [162], and so on.”
Modeling Radicalization Phenomena in Heterogeneous Populations (2015, background): “Some hints are outlined to favor novel public policies towards social integration.”
The structure and dynamics of multilayer networks (2014, methodology): “At variance with previous setups of voter model [286,296], each opinion or party is modeled here as one social network where the contagion dynamics takes place.”
Network resilience (2020, background): “The voter model is likely the simplest model for the spread of opinions with dynamics that may lead to consensus [537].”
Binary Opinion Dynamics with Stubborn Agents (2013, background): “…voter model on both in.nite lattices and .nite heterogenous topologies, as well as the biased voter model, where each individual has exogenous preferences on the possible choices ([Cox and Griffeath 1986; Gray 1986; Kearns and Tan 2008; Krapivsky 1992; Liggett 2005; Sood and Redner 2005]).”
Modelling dynamical processes in complex socio-technical systems (2011, result): “Finally, a wealth of surprising results, often overturning the common wisdom obtained by studies on regular networks, have been harvested on the voter and the Axelrod model”
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, background): “A variety of models were introduced to gain insights into binary-state dynamics on complex networks [42], such as the votermodels for competition of twoopinions [437], stochastic propagationmodels for epidemic spreading [438],models of rumor diffusion and adoption of new technologies [439], cascadin”
Critical phenomena in complex networks (2007, background): “Based on this conservation, Sood and Redner (2005) arrived at the following physical picture for the voter model on uncorrelated complex networks.”
Statistical physics of social dynamics (2007, neutral): “For networks with scale-free distributed degree (with exponent γ), TN scales then as N for γ > 3 and sublinearly for γ ≤ 3, in good agreement with numerical simulations (Castellano et al., 2005; Sood and Redner, 2005; Suchecki et al., 2005a).”
Homophily and Contagion Are Generically Confounded in Observational Social Network Studies (2010, background): “Probabilistically, the vector Y (t) is a Markov chain, specifically a variant of the “voter model” of statistical mechanics on a graph (Liggett, 1985; Sood and Redner, 2005); the minor addition of low-frequency noise (doing the opposite of the selected neighbor) keeps the homogeneous configurations…”
Binary-state dynamics on complex networks: pair approximation and beyond (2012, neutral): “Examples include models for competition between two opinions in a network-based population, such as the voter model [5,6] and the majority-vote model [5,7,8].”