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Register a new userTowards real-world complexity: an introduction to multiplex networks
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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.
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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.
We develop a theoretical framework for the study of epidemic-like social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks. Specifically, we propose a contact-based information spreading model, and show that the critical point of the multiplex system associated to the active phase is determined by the layer whose contact probability matrix has the largest eigenvalue. The framework is applied to a number of different situations, including a real multiplex system. Finally, we also show that when the system through which information is disseminating is inherently multiplex, working with the graph that results from the aggregation of the different layers is flawed.
We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address various notions of the network robustness relevant to multiplex networks such as the resilience of ordinary- and mutual connectivity under random or targeted node removals as well as the biconnectivity. We found that correlated coupling can affect the structural robustness of multiplex networks in diverse fashion. For example, for maximally-correlated duplex networks, all pairs of nodes in the giant component are connected via at least two independent paths and network structure is highly resilient to random failure. In contrast, anti-correlated duplex networks are on one hand robust against targeted attack on high-degree nodes, but on the other hand they can be vulnerable to random failure.
Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the systems structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of link overlap in the viability of multiplex networks, both analytically and numerically. Distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several removal strategies. Our results show that the link overlap strongly facilitates viability and mutual percolation; at the same time, the presence of link overlap poses challenge in analytical approach to the problem.
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural route to understand the dynamics, as well as to synthesize or optimize the functions, of networks. A broad spectrum of network structural patterns have been respectively reported in the past decade, such as communities, multipartites, hubs, authorities, outliers, bow ties, and others. Here, we show that most individual real-world networks demonstrate multiplex structures. That is, a multitude of known or even unknown (hidden) patterns can simultaneously situate in the same network, and moreover they may be overlapped and nested with each other to collaboratively form a heterogeneous, nested or hierarchical organization, in which different connective phenomena can be observed at different granular levels. In addition, we show that the multiplex structures hidden in exploratory networks can be well defined as well as effectively recognized within an unified framework consisting of a set of proposed concepts, models, and algorithms. Our findings provide a strong evidence that most real-world complex systems are driven by a combination of heterogeneous mechanisms that may collaboratively shape their ubiquitous multiplex structures as we observe currently. This work also contributes a mathematical tool for analyzing different sources of networks from a new perspective of unveiling multiplex structures, which will be beneficial to multiple disciplines including sociology, economics and computer science.
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