Mutually connected component of networks of networks with replica nodes

Bianconi, Ginestra; Dorogovtsev, S. N.; Mendes, J. F. F.

doi:10.1103/physreve.91.012804

Cited by 39 publications

(55 citation statements)

References 27 publications

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“…These methods are versatile, as they can be applied not only to ensembles of random networks, but also to single network realizations. For these reasons these algorithms are becoming increasingly popular in network science with applications ranging from percolation on single and multilayer networks to controllability [13,15,[34][35][36]43,47]. These algorithms proceed by iteration of dynamical rules, which determine messages or beliefs that a node sent to a neighboring node.…”

Section: A General Observations On the Message Passing Algorithm Formentioning

confidence: 99%

“…Networks of networks are multilayer networks formed by different networks (layers), where the nodes of different networks might be related by interdependencies. The percolation transition in these networks is significantly affected by the way the links implying interdependencies are placed, and, moreover, instead of single, there may be multiple transitions [34,35].…”

Section: Introductionmentioning

confidence: 99%

“…The emergence of the MCGC has been studied on a variety of multilayer structures including multiplex networks [11][12][13][28][29][30][31][32] and networks of networks [33][34][35]. Networks of networks are multilayer networks formed by different networks (layers), where the nodes of different networks might be related by interdependencies.…”

Section: Introductionmentioning

confidence: 99%

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Message passing theory for percolation models on multiplex networks with link overlap

2016

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Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

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Section: A General Observations On the Message Passing Algorithm Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Message passing theory for percolation models on multiplex networks with link overlap

2016

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“…Particularly noticeable has been the finding that when nodes of different networks are interdependent with each other, multilayer networks might be much more fragile than single networks and may have cascading failures that yield abrupt transitions [72,[75][76][77][78][79][80] . Therefore this result explains why global infrastructures are prone to dramatic avalanches of failures.…”

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confidence: 99%

“…It has been shown that considering the multilayer nature of networks can modify significantly the conclusions reached by considering single networks. A number of dynamical processes, including percolation [72,[75][76][77][78][79][80][81], diffusion [82], epidemic spreading [83] and game theory [84] present a phenomenology that is unexpected if one consider the layers in isolation. Moreover, it has been shown that multilayer networks are characterized by significant correlations [22,[85][86][87][88][89] in their structure that can change the dynamical properties of the multilayer network.…”

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confidence: 99%

Interdisciplinary and physics challenges of network theory

Bianconi¹

2015

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-Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.Introduction. -Network theory has emerged almost twenty years ago, as a new field for characterizing interacting complex systems, such as the Internet, the biological networks of the cell, and social networks. It is now time to reflect on the maturity of the field, indicating the main results obtained so far and the big challenges that lie ahead.Initially, the physics perspective, in particular the statistical mechanics approach, has dominated the field of Network Theory [1][2][3][4][5][6][7]. This point of view has played a central role to characterize the universal properties of the structure of complex networks. It has been found that despite the diversity of complex networks, ranging from the Internet to the protein interaction networks in the cell, most networks obey universal properties: they are small-world [9], they are scale-free [8], and they have a non trivial community structure [7]. Moreover, over the years, special attention has been addressed to the interplay between network structure and dynamics [10,11]. In fact phase diagrams of critical phenomena and dynamical processes change drastically when the dynamics is defined on complex networks. Complex networks are responsible for significant changes in the critical behaviour of percolation, Ising model, random walks, epidemic spreading, synchronization, and controllability of networks [10][11][12][13].The need to characterize complex systems, to extract relevant information from them, and to understand how dynamical processes are affected by network structure, has never been more severe than in the XXI century when we are witnessing a Big Data explosion in social sciences, information and communication technologies and in biology.

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