Heterogeneous pair approximation for voter models on networks

Pugliese, Emanuele; Castellano, Claudio

doi:10.1209/0295-5075/88/58004

Cited by 78 publications

(115 citation statements)

References 29 publications

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“…However, even after this rewiring, the match to MF theory is poor because dynamical correlations are still neglected. The recent PA theory for the voter model [4] (see also [5]) accounts for the dynamical correlations and hence gives a good match to the survival probability on the rewired network but not on the clustered original network.…”

Section: Voter Modelmentioning

confidence: 96%

Accuracy of mean-field theory for dynamics on real-world networks

et al. 2012

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Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of the theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as z = 4.

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Section: Voter Modelmentioning

confidence: 96%

Accuracy of mean-field theory for dynamics on real-world networks

et al. 2012

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“…It is therefore a powerful theory but only for specific network topologies. Our analysis may be improved upon, by modeling bipartite networks, networks with strong cliques, or using a more accurate pair approximation [5,56,57], but our goal here is to derive simple expressions that can describe some of the most interesting behavior. We give the details of the FPA in Appendix C and describe the main results here.…”

Section: Fokker-planck Approximation Of the Ccis Modelmentioning

confidence: 99%

“…Furthermore, this approximation breaks down for small k and small β, in which we show in Section V that the consensus time scales as β −1 . Future work could improve the accuracy of the current results with a pair approximation theory [56,57]. This paper mainly focuses on the outward process, but we have also compared theory and simulation for the other processes by varying β and k 2 , in Poisson and scale-free networks, while setting δ and µ to 0.…”

Section: Derivationmentioning

confidence: 99%

Competing opinions and stubborness: Connecting models to data

2016

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We introduce a general contagion-like model for competing opinions that includes dynamic resistance to alternative opinions. We show that this model can describe candidate vote distributions, spatial vote correlations, and a slow approach to opinion consensus with sensible parameter values. These empirical properties of large group dynamics, previously understood using distinct models, may be different aspects of human behavior that can be captured by a more unified model, such as the one introduced in this paper.

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“…Defining an exact law for the degree distribution allows finding analytical solutions to problems like the dynamics of diseases [42] or voters [43], through a heterogeneous mean field approximation. These problems can nevertheless still be analysed when networks are not exactly scale-free by means of numerical simulations.…”

Section: Common Pitfalls and Misleadingmentioning

confidence: 99%

Studying the Topology of Transportation Systems through Complex Networks: Handle with Care

Zanin

Sun

Wandelt

2018

Journal of Advanced Transportation

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The introduction of complex network concepts in the study of transportation systems has supposed a paradigm shift and has allowed understanding different transport phenomena as the emergent result of the interactions between the elements composing them. In spite of several notable achievements, lurking pitfalls are undermining our understanding of the topological characteristics of transportation systems. In this study, we analyse four of the most common ones, specifically related to the assessment of the scale-freeness of networks, the interpretation and comparison of topological metrics, the definition of a node ranking, and the analysis of the resilience against random failures and targeted attacks. For each topic we present the problem from both a theoretical and operational perspective, for then reviewing how it has been tackled in the literature and finally proposing a set of solutions. We further use six real-world transportation networks as case studies and discuss the implications of these four pitfalls in their analysis. We present some future lines of work that are stemming from these pitfalls and that will allow a deeper understanding of transportation systems from a complex network perspective.

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Heterogeneous pair approximation for voter models on networks

Cited by 78 publications

References 29 publications

Accuracy of mean-field theory for dynamics on real-world networks

Accuracy of mean-field theory for dynamics on real-world networks

Competing opinions and stubborness: Connecting models to data

Studying the Topology of Transportation Systems through Complex Networks: Handle with Care

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