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Multilayer networks
 TOOL FOR MULTILAYER ANALYSIS AND VISUALIZATION OF NETWORKS 17 OF 18
, 2014
"... In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is impo ..."
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Cited by 34 (7 self)
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In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such “multilayer” features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize “traditional ” network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary
ARTICLE Multiple tipping points and optimal repairing in interacting networks
"... Systems composed of many interacting dynamical networkssuch as the human body with its biological networks or the global economic network consisting of regional clustersoften exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread ..."
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Systems composed of many interacting dynamical networkssuch as the human body with its biological networks or the global economic network consisting of regional clustersoften exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two 'forbidden' transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between welldefined states, in agreement with the predictions of our model.
The structure and dynamics of multilayer networks
, 2014
"... In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all component ..."
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In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal or contextrelated properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of realworld systems,
A Critical Review of Robustness in Power Grids Using Complex Networks Concepts
 ENERGIES
, 2015
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On the Dynamics of Cascading Failures in Interdependent Networks
, 2012
"... Cascading failures in interdependent networks have been investigated using percolation theory in recent years. Here, we study the dynamics of the cascading failures, the average and fluctuations of the number of cascading as a function of system size N near criticality. The system we analyzed is a p ..."
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Cascading failures in interdependent networks have been investigated using percolation theory in recent years. Here, we study the dynamics of the cascading failures, the average and fluctuations of the number of cascading as a function of system size N near criticality. The system we analyzed is a pair of fully interdependent ErdösRényi (ER) networks. We show that when p is close to pc, the whole dynamical process of cascading failures can be divided into three time stages. The giant component sizes in the second time stage, presented by a plateau in the size of giant component, have large standard deviations, which cannot be well predicted by the meanfield theory. We also investigate the standard deviation of the total time std(τ) using simulations. When p = pc, our numerical simulations indicate that std(τ)∼N 1/3, which increases faster than the mean,<τ> ∼ N 1/4, predicted by the meanfield theory. We also find the scaling behavior as a function of N and p of<τ> and std(τ) for p< pc. 1
RESEARCH ARTICLE Quantifying the Role of Homophily in Human Cooperation Using Multiplex Evolutionary Game Theory
"... ☯ These authors contributed equally to this work. ..."
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Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependency
, 2014
"... Increased coupling between critical infrastructure networks, such as power and communications, has important implications for the reliability and security of these networks. To understand the implications of powercommunications coupling, researchers have studied interdependent network models and ..."
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Increased coupling between critical infrastructure networks, such as power and communications, has important implications for the reliability and security of these networks. To understand the implications of powercommunications coupling, researchers have studied interdependent network models and reported that increased coupling can increase system vulnerability [1, 2]. However, these results come from models that have substantially different mechanisms of cascading, relative to those found in actual power and communications networks. This paper reports on two sets of experiments that compare the network vulnerability implications resulting from simple topological models and models that more accurately capture the dynamics of cascading in power systems. In the first set of experiments, we compare a simple model of intranetwork cascading to a power grid model and find that the power grid model reveals that power grids have a higher level of vulnerability, relative to what would be inferred from a topological contagion model. In a second set of experiments, we compare the coupled topological model from [1] to three different physicsbased models of power grids coupled to communication networks. Again, the results show that more accurate models lead to very different conclusions. In all but the most extreme case, the physicsbased power grid models suggest that increased powercommunications coupling decreases vulnerability. This is opposite from what one would conclude from the model in [1], in which zero coupling is optimal. Finally, an extreme case, in which communications