We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited the performance methods as applied ad hoc networks with known structure, compared. find that most accurate tend be more computationally expensive, both aspects need considered when choosing a method for practical purposes. work intended an introduction well proposal standard benchmark test detection methods.

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types relationships, change time include complications. Such systems subsystems layers connectivity, it is important to take such 'multilayer' features into account try improve our understanding complex systems. Consequently, necessary generalize 'traditional' network theory by developing (and validating) framework associated tools study multilayer...

We propose a method to find the community structure in complex networks based on an extremal optimization of value modularity. The outperforms optimal modularity found by existing algorithms literature giving better understanding structure. present results algorithm for computer-simulated and real compare them with other approaches. efficiency accuracy make it feasible be used accurate identification large networks.

We propose a procedure for analyzing and characterizing complex networks. apply this to the social network as constructed from email communications within medium sized university with about 1700 employees. Email networks provide an accurate nonintrusive description of flow information human organizations. Our results reveal self-organization into state where distribution community sizes is self-similar. This suggests that universal mechanism, responsible emergence scaling in other...

A network representation is useful for describing the structure of a large variety complex systems. However, most real and engineered systems have multiple subsystems layers connectivity, data produced by such very rich. Achieving deep understanding necessitates generalizing "traditional" theory, newfound deluge now makes it possible to test increasingly general frameworks study networks. In particular, although adjacency matrices are describe traditional single-layer networks, insufficient...

We present the analysis of interrelation between two processes accounting for spreading an epidemics, and information awareness to prevent its infection, on top multiplex networks. This scenario is representative epidemic process a network persistent real contacts, cyclic diffusing in virtual social contacts same individuals. The topology corresponds where diffusive are interacting affecting each other. using Microscopic Markov Chain Approach (MMCA) reveals phase diagram incidence epidemics...

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. a set of networks linked through interconnected layers. To this end, we propose construction supra-Laplacian matrix, which consists dimensional lifting Laplacian matrix each layer network. use perturbative analysis reveal analytically structure eigenvectors and eigenvalues complete network in terms spectral properties individual The spectrum allows us understand physics diffusion-like top networks.

We study the relationship between topological scales and dynamic time in complex networks. The analysis is based on full dynamics towards synchronization of a system coupled oscillators. In process, modular structures corresponding to well defined communities nodes emerge different scales, ordered hierarchical way. also provides useful connection dynamics, networks topology spectral graph analysis.

We propose a class of models social network formation based on mathematical abstraction the concept distance. Social distance attachment is represented by tendency peers to establish acquaintances via decreasing function relative in representative space. derive analytical results (corroborated extensive numerical simulations), showing that model reproduces main statistical characteristics real networks: large clustering coefficient, positive degree correlations, and emergence hierarchy...

Explosive collective phenomena have attracted much attention since the discovery of an explosive percolation transition. In this Letter, we demonstrate how transition shows up in synchronization scale-free networks by incorporating a microscopic correlation between structural and dynamical properties system. The characteristics are analytically studied star graph reproducing results obtained synthetic networks. Our findings represent first abrupt complex provide deeper understanding roots...

The problem of searchability in decentralized complex networks is great importance computer science, economy, and sociology. We present a formalism that able to cope simultaneously with the search congestion effects arise when parallel searches are performed, we obtain expressions for average cost both presence absence congestion. This used optimal network structures system using local algorithm. It found only two classes can be optimal: starlike configurations, number small,...

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven network with thousands interactions each. A fundamental open question is then how much information really necessary accurately represent structure multilayer system, if when layers indeed aggregated. Here we introduce method, based theory, reduce...

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed the physics literature, so-called contact process (CP) where contagion is expanded at a certain rate from an infected vertex to one neighbor time, and reactive (RP) which individual effectively all its neighbors expand epidemics. However, more realistic scenario obtained interpolation between these cases, considering number of per unit time. Here we...

Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected under random failures", we extend well-known walks multiplexes and introduce a new type walk that can exist only in multiplexes. We derive exact expressions vertex occupation time coverage. Finally, show how efficiency exploring multiplex critically depends...

Modular structure is ubiquitous in real-world complex networks, and its detection important because it gives insights into the structure–functionality relationship. The standard approach based on optimization of a quality function, modularity, which relative measure for partition network modules. Recently, some authors (Fortunato Barthélemy 2007 Proc. Natl Acad. Sci. USA 104 36 Kumpula et al Eur. Phys. J. B 56 41) have pointed out that modularity has fundamental drawback: existence...

We present a simple model of communication in networks with hierarchical branching. analyze the behavior from viewpoint critical systems under different situations. For certain values parameters, continuous phase transition between sparse and congested regime is observed accurately described by an order parameter power spectra. At point totally independent number levels. Also scaling properties are when size system varies. The presence noise shown to break transition. analytical results...

We study evolutionary game dynamics on structured populations in which individuals take part several layers of networks interactions simultaneously. This multiplex interdependent accounts for the different kind social ties each individual has. By coupling a Prisoner's Dilemma networks, we show that resilience cooperative behaviors extremely large values temptation to defect is enhanced by structure. Furthermore, this intrinsically related non-trivial organization cooperation across network...

The determination of the most central agents in complex networks is important because they are responsible for a faster propagation information, epidemics, failures and congestion, among others. A challenging problem to identify them networked systems characterized by different types interactions, forming interconnected multilayer networks. Here we describe mathematical framework that allows us calculate centrality such rank nodes accordingly, finding ones play roles cohesion whole...

The understanding of emergent collective phenomena in natural and social systems has driven the interest scientists from different disciplines during decades. Among these phenomena, synchronization a set interacting individuals or units been intensively studied because its ubiquity world. In this Letter, we show how for fixed coupling strengths local patterns emerge differently homogeneous heterogeneous complex networks, driving process towards certain global degree following paths....

Epidemic-like spreading processes on top of multilayered interconnected complex networks reveal a rich phase diagram intertwined competition effects. A recent study by the authors [Granell et al. Phys. Rev. Lett. 111, 128701 (2013)] presented analysis interrelation between two accounting for an epidemics, and information awareness to prevent its infection, multiplex networks. The results in case which implies total immunization disease, revealed existence metacritical point at critical onset...

Unveiling the community structure of networks is a powerful methodology to comprehend interconnected systems across social and natural sciences. To identify different types functional modules in interaction data aggregated single network layer, researchers have developed many methods. For example, flow-based methods proven useful for identifying modular dynamics weighted directed that capture constraints on flow they represent. However, networked consist agents or components exhibit multiple...

Current modeling of infectious diseases allows for the study realistic scenarios that include population heterogeneity, social structures and mobility processes down to individual level. The advances in realism epidemic description call explicit behavioral responses presence disease within frameworks. Here we formulate analyze a metapopulation model incorporates several self-initiated changes into patterns individuals. We find prevalence-based travel limitations do not alter invasion...