Disease Spreading in Structured Scale-Free Networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading.Comment: 7 pages, 6 figures. EPJ styl

Multilayer Networks in a Nutshell

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's constituents. During the last two decades, network science has provided many insights in natural, social, biological and technological systems. However, real systems are more often than not interconnected, with many interdependencies that are not properly captured by single layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio

From Scale-free to Erdos-Renyi Networks

We analyze a model that interpolates between scale-free and Erdos-Renyi networks. The model introduced generates a one-parameter family of networks and allows to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.Comment: 8 pages, 6 figure

Immunization of Real Complex Communication Networks

Most communication networks are complex. In this paper, we address one of the fundamental problems we are facing nowadays, namely, how we can efficiently protect these networks. To this end, we study an immunization strategy and found that it works as good as targeted immunization, but using only local information about the network topology. Our findings are supported with numerical simulations of the Susceptible-Infected-Removed (SIR) model on top of real communication networks, where immune nodes are previously identified by a covering algorithm. The results provide useful hints in the way to design and deploying a digital immune system.Comment: 6 pages. To appear in the European Physical Journal B (2006

Heterogeneous resource allocation can change social hierarchy in public goods games

Public Goods Games represent one of the most useful tools to study group interactions between individuals. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution - known as Pareto Law - and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of Public Goods Games that allows for the emergence of both of these features from first principles. Unlike traditional Public Goods Games on networks, where players contribute equally to all the games in which they participate, we allow individuals to redistribute their contribution according to what they earned in previous rounds. Results from numerical simulations show that not only a Pareto distribution for the payoffs naturally emerges but also that if players don't invest enough in one round they can act as defectors even if they are formally cooperators. Finally, we also show that the players self-organize in a very productive backbone that covers almost perfectly the minimum spanning tree of the underlying interaction network. Our results not only give an explanation for the presence of the wealth heterogeneity observed in real data but also points to a conceptual change regarding how cooperation is defined in collective dilemmas.Comment: 8 pages, 5 figures, 55 reference

Directionality reduces the impact of epidemics in multilayer networks

The study of how diseases spread has greatly benefited from advances in network modeling. Recently, a class of networks known as multilayer graphs has been shown to describe more accurately many real systems, making it possible to address more complex scenarios in epidemiology such as the interaction between different pathogens or multiple strains of the same disease. In this work, we study in depth a class of networks that have gone unnoticed up to now, despite of its relevance for spreading dynamics. Specifically, we focus on directed multilayer networks, characterized by the existence of directed links, either within the layers or across layers. Using the generating function approach and numerical simulations of a stochastic susceptible-infected-susceptible (SIS) model, we calculate the epidemic threshold for these networks for different degree distributions of the networks. Our results show that the main feature that determines the value of the epidemic threshold is the directionality of the links connecting different layers, regardless of the degree distribution chosen. Our findings are of utmost interest given the ubiquitous presence of directed multilayer networks and the widespread use of disease-like spreading processes in a broad range of phenomena such as diffusion processes in social and transportation systems.Comment: 20 pages including 7 figures. Submitted for publicatio