Results 1 
9 of
9
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 ..."
Abstract

Cited by 34 (7 self)
 Add to MetaCart
(Show Context)
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
to multiplex networks
, 2015
"... Towards realworld complexity: an introduction ..."
(Show Context)
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 ..."
Abstract
 Add to MetaCart
(Show Context)
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 ..."
Abstract
 Add to MetaCart
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,
Regular Article THE EUROPEAN
, 2014
"... Interdependent networks: vulnerability analysis and strategies to limit cascading failure ..."
Abstract
 Add to MetaCart
Interdependent networks: vulnerability analysis and strategies to limit cascading failure
Link overlap, viability, and mutual percolation in multiplex networks
"... Many realworld complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system’s structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of link overlap across layers despite stro ..."
Abstract
 Add to MetaCart
(Show Context)
Many realworld complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system’s 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 nonoverlapping 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.
RESEARCH ARTICLE Percolation on Networks with Conditional Dependence Group
"... Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break t ..."
Abstract
 Add to MetaCart
(Show Context)
Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well.
Environmental
, 2014
"... Network science has attracted much attention in recent years due to its interdisciplinary applications. We witnessed the revolution of network science in 1998 and 1999 started with smallworld and scalefree networks having now thousands of highprofile publications, and it seems that since 2010 stu ..."
Abstract
 Add to MetaCart
(Show Context)
Network science has attracted much attention in recent years due to its interdisciplinary applications. We witnessed the revolution of network science in 1998 and 1999 started with smallworld and scalefree networks having now thousands of highprofile publications, and it seems that since 2010 studies of ‘network of networks ’ (NON), sometimes called multilayer networks or multiplex, have attracted more and more attention.The analytic framework for NON yields a novel percolation law for n interdependent networks that shows that percolation theory of single networks studied extensively in physics and mathematics in the last 50 years is a specific limit of the rich and very different general case of n coupled networks. Since then, properties and dynamics of interdependent and interconnected networks have been studied extensively, and scientists are finding many interesting results and discovering many surprising phenomena. Because most natural and engineered systems are composed of multiple subsystems and layers of connectivity, it is important to consider these features in order to improve our understanding of such complex systems. Now the study of NON has become one of the important directions in network science. In this paper, we review recent studies on the new emerging area—NON. Due to the fast growth of this field, there are many definitions of different types of NON, such as interdependent networks,