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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
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 33 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson
Do topological models provide good information about electricity infrastructure vulnerability
, 2010
"... In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path leng ..."
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Cited by 30 (3 self)
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In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern US power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack vectors that appear to cause the most damage depend on the measure chosen. While our topological and power grid model results show some trends that are similar, there is only a mild correlation between the vulnerability measures for individual simulations. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading. Electricity infrastructures are vital to the operation of modern society, yet they are notably vulnerable to cascading failures. Understanding the nature of this vulnerability is fundamental to the assessment of electric energy reliability and security. A number of articles have recently used topological
Evolutionary game theory: temporal and spatial effects beyond replicator dynamics
, 2009
"... Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the socalled replicator equation, that describes mathematically the idea that those indiv ..."
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Cited by 28 (1 self)
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Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the socalled replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of nonmean field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the nontrivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.
Hierarchical small worlds in software architecture
 Dynamics of Continuous Discrete and Impulsive Systems: Series B; Applications and Algorithms
, 2007
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TOPOLOGICAL VULNERABILITY OF THE EUROPEAN POWER GRID UNDER ERRORS AND ATTACKS
, 2006
"... We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirtythree different networks. Though every power grid studied has exponenti ..."
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Cited by 22 (0 self)
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We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirtythree different networks. Though every power grid studied has exponential degree distribution and most of them lack typical smallworld topology, they display patterns of reaction to node loss similar to those observed in scalefree networks. We have found that the node removal behavior can be logarithmically related to the power grid size. This logarithmic behavior would suggest that, though size favors fragility, growth can reduce it. We conclude that, with the evergrowing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order to facilitate and improve the power grid design and functioning.
Spontaneous emergence of modularity in cellular networks
"... Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the forma ..."
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Cited by 21 (1 self)
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Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such a selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.
Conditions for synchronizability in arrays of coupled linear systems
 IEEE Transactions on Automatic Control
"... Synchronization control in arrays of identical outputcoupled continuoustime linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable systems that are detectable form their outputs, a linear feedbac ..."
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Cited by 18 (2 self)
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Synchronization control in arrays of identical outputcoupled continuoustime linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable systems that are detectable form their outputs, a linear feedback law exists under which any number of coupled systems synchronize provided that the (directed, weighted) graph describing the interconnection is fixed and connected. An algorithm generating one such feedback law is presented. It is also shown that for critically unstable systems detectability is not sufficient, whereas fullstate coupling is, for the existence of a linear feedback law that is synchronizing for all connected coupling configurations. 1