Information transfer in community structured multiplex networks

The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.). The mathematical description of these interacting networks has been coined under the name of multilayer networks, where each layer accounts for a type of interaction. It has been shown that diffusive processes on top of these networks present a phenomenology that cannot be explained by the naive superposition of single layer diffusive phenomena but require the whole structure of interconnected layers. Nevertheless, the description of diffusive phenomena on multilayer networks has obviated the fact that social networks have strong mesoscopic structure represented by different communities of individuals driven by common interests, or any other social aspect. In this work, we study the transfer of information in multilayer networks with community structure. The final goal is to understand and quantify, if the existence of well-defined community structure at the level of individual layers, together with the multilayer structure of the whole network, enhances or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure

Pulsating-campaigns of human prophylaxis driven by risk perception palliate oscillations of direct contact transmitted diseases

Human behavioral responses play an important role in the impact of disease outbreaks and yet they are often overlooked in epidemiological models. Understanding to what extent behavioral changes determine the outcome of spreading epidemics is essential to design effective intervention policies. Here we explore, analytically, the interplay between the personal decision to protect oneself from infection and the spreading of an epidemic. We do so by coupling a decision game based on the perceived risk of infection with a Susceptible-Infected-Susceptible model. Interestingly, we find that the simple decision on whether to protect oneself is enough to modify the course of the epidemics, by generating sustained steady oscillations in the prevalence. We deem these oscillations detrimental, and propose two intervention policies aimed at modifying behavioral patterns to help alleviate them. Surprisingly, we find that pulsating campaigns, compared to continuous ones, are more effective in diminishing such oscillations.Comment: 19 pages, 6 figure

Benchmark model to assess community structure in evolving networks

Detecting the time evolution of the community structure of networks is crucial to identify major changes in the internal organization of many complex systems, which may undergo important endogenous or exogenous events. This analysis can be done in two ways: considering each snapshot as an independent community detection problem or taking into account the whole evolution of the network. In the first case, one can apply static methods on the temporal snapshots, which correspond to configurations of the system in short time windows, and match afterwards the communities across layers. Alternatively, one can develop dedicated dynamic procedures, so that multiple snapshots are simultaneously taken into account while detecting communities, which allows us to keep memory of the flow. To check how well a method of any kind could capture the evolution of communities, suitable benchmarks are needed. Here we propose a model for generating simple dynamic benchmark graphs, based on stochastic block models. In them, the time evolution consists of a periodic oscillation of the system's structure between configurations with built-in community structure. We also propose the extension of quality comparison indices to the dynamic scenario.Comment: 11 pages, 7 figures, 3 table

Hierarchical multiresolution method to overcome the resolution limit in complex networks

The analysis of the modular structure of networks is a major challenge in complex networks theory. The validity of the modular structure obtained is essential to confront the problem of the topology-functionality relationship. Recently, several authors have worked on the limit of resolution that different community detection algorithms have, making impossible the detection of natural modules when very different topological scales coexist in the network. Existing multiresolution methods are not the panacea for solving the problem in extreme situations, and also fail. Here, we present a new hierarchical multiresolution scheme that works even when the network decomposition is very close to the resolution limit. The idea is to split the multiresolution method for optimal subgraphs of the network, focusing the analysis on each part independently. We also propose a new algorithm to speed up the computational cost of screening the mesoscale looking for the resolution parameter that best splits every subgraph. The hierarchical algorithm is able to solve a difficult benchmark proposed in [Lancichinetti & Fortunato, 2011], encouraging the further analysis of hierarchical methods based on the modularity quality function

Exploratory data analysis using network based techniques

The aim of this document is to present the work done during the development of my master thesis. The work belongs to the field of complex networks, more concretely to the detection of communities in complex networks. Chapter 1 will be an introduction of the basic concepts and motivations of this work, mainly clarifying the fields of exploratory data analysis, data clustering and complex networks. As all the work is about the finding of communities in complex networks, Chapter 2 is devoted to explain the concepts of mesoscopic structure of networks and its importance in the analysis of real networks, along with the explanations of some of the most well-known techniques to perform this analysis. All the progress done during the master thesis relies on a method for detecting communities developed in the past years by the research group I belong to. This method is known as the AFG algorithm, named after the three authors Arenas, Fernández and Gómez, and it is explained in section 2.5.2 with special emphasis. The work that I have developed is composed of two separate problems: the first one consists in designing an application to make possible the use of the AFG community detection method to perform data clustering over real world multidimensional datasets, which is explained in Chapter 3. The second work consists in improving the AFG method to make possible the detection of communities even when the difference of sizes of the communities make their detection impossible for other community detection algorithms, which can be found in Chapter 4. Chapter 5 contains the conclusions and the future lines of research derived from the present work, and in the Appendix there is a list of publications that sustain the contents presented in this document