Absorbing and shattered fragmentation transitions in multilayer coevolution

Diakonova, Marina; Miguel, M. San; Eguı́luz, Vı́ctor M.

doi:10.1103/physreve.89.062818

Cited by 59 publications

(88 citation statements)

References 34 publications

(54 reference statements)

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“…Fragmentation is the phenomenon in which a network might undergo a transition from a state where almost all nodes belong to a single giant component to a fragmented state in which the network breaks into several components. The fragmentation transition is a phenomenon generically associated with co-evolution network dynamics [29][30][31][32][33][34]. Here we consider the voter model (VM) [35,36] as a paradigmatic example.…”

Section: Introductionmentioning

confidence: 99%

“…In an extension of the CVM to multiplex networks (MCVM) some, but not all, nodes are interconnected across layers. Such nodes then have the same internal states in both layers [33]. This MCVM has an anomalous transition called shattered fragmentation in which one layer assumes a fragmented state whose topological properties would be different under the same model parameters in a single layer CVM.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that the driving force behind this transition is the asymmetry between re-wiring probabilities in different network layers, i.e. the individual lifetime of links in each of the layers [33].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical origins of the community structure of an online multi-layer society

et al. 2016

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Social structures emerge as a result of individuals managing a variety of different social relationships. Societies can be represented as highly structured dynamic multiplex networks. Here we study the dynamical origins of the specific community structures of a large-scale social multiplex network of a human society that interacts in a virtual world of a massive multiplayer online game. There we find substantial differences in the community structures of different social actions, represented by the various layers in the multiplex network. Community sizes distributions are either fat-tailed or appear to be centered around a size of 50 individuals. To understand these observations we propose a voter model that is built around the principle of triadic closure. It explicitly models the co-evolution of node-and link-dynamics across different layers of the multiplex network. Depending on link and node fluctuation probabilities, the model exhibits an anomalous shattered fragmentation transition, where one layer fragments from one large component into many small components. The observed community size distributions are in good agreement with the predicted fragmentation in the model. This suggests that several detailed features of the fragmentation in societies can be traced back to the triadic closure processes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical origins of the community structure of an online multi-layer society

et al. 2016

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“…Our analysis can be naturally cast in the framework of multiplex networks [24][25][26][27], which has recently proven successful for a more realistic modeling of different social dynamics [28][29][30][31][32][33]. According to this framework, agents are represented by nodes connected by links of different nature, where links of the same kind belong to the same layer of the system.…”

Section: Introductionmentioning

confidence: 99%

Interplay between consensus and coherence in a model of interacting opinions

Battiston

Cairoli

Nicosia

et al. 2016

Physica D: Nonlinear Phenomena

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The formation of agents' opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand, the concurrent participation of agents to discussions on different topics induces each agent to develop a coherent set of opinions across all the topics in which he is active. Moreover, the prevasive action of external stimuli, such as mass media, pulls the entire population towards a specific configuration of opinions on different topics. Here we propose a model in which agents with interrelated opinions, interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhood, strive to maintain internal coherence, due to the fact that each agent identifies meaningful relationships among its opinions on the different topics, and are at the same time subject to external fields, resembling the pressure of mass media. We show that the presence of heterogeneity in the internal coupling assigned by agents to their different opinions allows to obtain states with mixed levels of consensus, still ensuring that all the agents attain a coherent set of opinions. Furthermore, we show that all the observed features of the model are preserved in the presence of thermal noise up to a critical temperature, after which global consensus is no longer attainable. This suggests the relevance of our results for real social systems, where noise is inevitably present in the form of information uncertainty and misunderstandings. The model also demonstrates how mass media can be effectively used to favour the propagation of a chosen set of opinions, thus polarising the consensus of an entire population.

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“…Its usefulness extends from finance [15][16][17] and mobility [18,19], to epidemics [20,21] and societal dynamics [22][23][24][25][26][27][28]. The multiplex scenario is ostensibly non-trivial, in the sense that the phenomena observed on this system of interconnected networks cannot be straightforwardly reduced to an aggregate network [29].…”

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confidence: 99%

Dynamical leaps due to microscopic changes in multilayer networks

Diakonova¹,

Ramasco²,

Eguı́luz³

2017

EPL

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Recent developments of the multiplex paradigm included efforts to understand the role played by the presence of several layers on the dynamics of processes running on these networks. The possible existence of new phenomena associated to the richer topology has been discussed and examples of these differences have been systematically searched. Here, we show that the interconnectivity of the layers may have an important impact on the speed of the dynamics run in the network and that microscopic changes such as the addition of one single inter-layer link can notably affect the arrival at a global stationary state. As a practical verification, these results obtained with spectral techniques are confirmed with a Kuramoto dynamics for which the synchronization consistently delays after the addition of single inter-layer links.The ubiquity of processes naturally described by dynamics on networks raises important issues on the role played by network structure on the emergence of collective phenomena. It has been shown that spectral analysis of the associated adjacency and Laplacian matrices can offer insights into a variety of fundamental phenomena such as those relying upon spreading or diffusion mechanisms [1][2][3]. In particular, spectral methods are the basis to characterize synchronization and random walk diffusion in networks [4][5][6][7]. The second smallest eigenvalue λ 2 is known to be related to the timescale to synchronization [8] and consensus [9], and is often interpreted as the 'proper time' of the system to relax [10]. This quantity, which depending on the literature is known as 'algebraic connectivity' or 'spectral gap', is also indicative of the time of diffusion [11]. While the role of λ 2 in "simple" graphs is well understood, more effort is needed to characterize its role and behavior in more realistic (and therefore complex) contexts.One such novel framework is that of a multilayer network [12][13][14]. Its usefulness extends from finance [15][16][17] and mobility [18,19], to epidemics [20,21] and societal dynamics [22][23][24][25][26][27][28]. The multiplex scenario is ostensibly non-trivial, in the sense that the phenomena observed on this system of interconnected networks cannot be straightforwardly reduced to an aggregate network [29]. The implication is that the multiplex structure plays a fundamental role in diffusive processes, and that therefore its effect of on λ 2 is a pertinent and open issue.Diffusion on a multiplex, that is, a system with layers of N nodes with an association of corresponding nodes in each layer, were considered in [30,31]. By varying the inter-layer diffusion constant, these works found boundaries of λ 2 for the multiplex in terms of the values for individual layers (see also [32]). For a general weighted two-layer multiplex with a varying inter-layer link weight p, these results were rephrased in terms of a structural transition [33]: it was found that below some critical p c , λ 2 (p) ∼ 2 p, while for larger p the algebraic connectivity approaches an asymptote given...

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Absorbing and shattered fragmentation transitions in multilayer coevolution

Cited by 59 publications

References 34 publications

Dynamical origins of the community structure of an online multi-layer society

Dynamical origins of the community structure of an online multi-layer society

Interplay between consensus and coherence in a model of interacting opinions

Dynamical leaps due to microscopic changes in multilayer networks

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