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Register a new userAccuracy of Mean-Field Theory for Dynamics on Real-World Networks
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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 4.
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Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the systems structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.
We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.
We investigate the long-time properties of a dynamic, out-of-equilibrium, network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, which is a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we study in detail how the sizes of the communities and the degree of homophily/heterophily affects the network structure. In particular, we show that when the network is subject to enough heterophily, an overwhelming transition occurs: individuals of the smaller community are overwhelmed by links from agents of the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by obtaining the networks total and joint degree distributions, as well as the fraction of links across both communities and that of agents having less edges than the preferred degree. We use our mean-field theory to discuss the networks polarization when the group sizes and level of homophily vary.
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabasi-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.
Social network based information campaigns can be used for promoting beneficial health behaviours and mitigating polarisation (e.g. regarding climate change or vaccines). Network-based intervention strategies typically rely on full knowledge of network structure. It is largely not possible or desirable to obtain population-level social network data due to availability and privacy issues. It is easier to obtain information about individuals attributes (e.g. age, income), which are jointly informative of an individuals opinions and their social network position. We investigate strategies for influencing the system state in a statistical mechanics based model of opinion formation. Using synthetic and data based examples we illustrate the advantages of implementing coarse-grained influence strategies on Ising models with modular structure in the presence of external fields. Our work provides a scalable methodology for influencing Ising systems on large graphs and the first exploration of the Ising influence problem in the presence of ambient (social) fields. By exploiting the observation that strong ambient fields can simplify control of networked dynamics, our findings open the possibility of efficiently computing and implementing public information campaigns using insights from social network theory without costly or invasive levels of data collection.
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