Voter model on networks partitioned into two cliques of arbitrary sizes

Abstract

The voter model is an archetypal stochastic process that represents opinion dynamics. In each update, one agent is chosen uniformly at random. The selected agent then copies the current opinion of a randomly selected neighbour. We investigate the voter model on a network with an exogenous community structure: two cliques (i.e. complete subgraphs) randomly linked by $X$ interclique edges. We show that, counterintuitively, the mean consensus time is typically not a monotonically decreasing function of $X$. Cliques of fixed proportions with opposite initial opinions reach a consensus, on average, most quickly if $X$ scales as $N^{3/2}$, where $N$ is the number of agents in the network. Hence, to accelerate a consensus between cliques, agents should connect to more members in the other clique as $N$ increases but not to the extent that cliques lose their identity as distinct communities. We support our numerical results with an equation-based analysis. By interpolating between two asymptotic heterogeneous mean-field approximations, we obtain an equation for the mean consensus time that is in excellent agreement with simulations for all values of $X$.

arXiv commentUpdated bibliography. To appear in Journal of Physics A: Mathematical and Theoretical

References in corpus (42)

• Finding and evaluating community structure in networks
• Statistical physics of social dynamics
• Community detection in networks: A user guide
• Finding statistically significant communities in networks
• Voter Model on Heterogeneous Graphs
• Spectral redemption: clustering sparse networks
• Voter Models on Heterogeneous Networks
• Uncovering space-independent communities in spatial networks
• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Characterizing the community structure of complex networks
• The non-linear q-voter model
• Is the Voter Model a model for voters?
• Incomplete ordering of the voter model on small-world networks
• Reality Inspired Voter Models: A Mini-Review
• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Opinion dynamics: models, extensions and external effects
• Ordering dynamics with two non-excluding options: Bilingualism in language competition
• Heterogeneous Voter Models
• Solution of voter model dynamics on annealed small-world networks
• Ultimate Fate of Constrained Voters
• Irreducibility of multilayer network dynamics: the case of the voter model
• Statistical Physics Of Opinion Formation: is it a SPOOF?
• Efficient method for estimating the number of communities in a network
• Voter model on the two-clique graph
• Voter models on weighted networks
• Anomalous lifetime distributions and topological traps in ordering dynamics
• Population genetics on islands connected by an arbitrary network: An analytic approach
• Effect of network topology on the ordering dynamics of voter models
• Estimating the number of communities in networks by spectral methods
• Consensus time in a voter model with concealed and publicly expressed opinions
• Voter model with non-Poissonian interevent intervals
• Dynamics of Vacillating Voters
• Dynamics on networks: competition of temporal and topological correlations
• Fast-mode elimination in stochastic metapopulation models
• Conservation laws for voter-like models on directed networks
• Heterogenous mean-field analysis of a generalized voter-like model on networks
• Opinion Formation under Antagonistic Influences
• Timing interactions in social simulations: The voter model
• Eigenvector dynamics under perturbation of modular networks
• The Ising chain constrained to an even or odd number of positive spins

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