MuxViz: A Tool for Multilayer Analysis and Visualization of Networks

Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyze and interactively visualize multilayer data using empirical genetic, neuronal, and transportation networks. Our software is available at https://github.com/manlius/muxViz.Comment: 18 pages, 10 figures (text of the accepted manuscript

Suppressing disease spreading by using information diffusion on multiplex networks

Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic numerical simulations suggest that an information outbreak can be triggered in a communication network by its own spreading dynamics or by a disease outbreak on a contact network, but that the disease threshold is not affected by information spreading. Our key finding is that there is an optimal information transmission rate that markedly suppresses the disease spreading. We find that the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world spreading processes at the optimal information transmission rate.Comment: 11 pages, 8 figure

Latent space models for multidimensional network data

Network data are any relational data recorded among a group of individuals, the nodes. When multiple relations are recorded among the same set of nodes, a more complex object arises, which we refer to as “multidimensional network”, or “multiplex”, where different relations corresponding to different networks. In the past, statistical analysis of networks has mainly focused on single-relation network data, referring to a single relation of interest. Only in recent years statistical models specifically tailored for multiplex data begun to be developed. In this context, only a few works have been introduced in the literature with the aim at extending the latent space modeling framework to multiplex data. Such framework postulates that nodes may be characterized by latent positions in a p-dimensional Euclidean space and that the presence/absence of an edge between any two nodes depends on such positions. When considering multidimensional network data, latent space models can help capture the associations between the nodes and summarize the observed structure in the different networks composing a multiplex. This dissertation discusses some latent space models for multidimensional network data, to account for different features that observed multiplex data may present. A first proposal allows to jointly represent the different networks into a single latent space, so that average similarities between the nodes may be captured as proximities in such space. A second work introduces a class of latent space models with node-specific effects, in order to deal with different degrees of heterogeneity within and between networks in multiplex data, corresponding to different types of node-specific behaviours. A third work addresses the issue of clustering of the nodes in the latent space, a frequently observed feature in many real world network and multidimensional network data. Here, clusters of nodes in the latent space correspond to communities of nodes in the multiplex. The proposed models are illustrated both via simulation studies and real world applications, to study their perfomances and abilities

Modelling heterogeneity in Latent Space Models for Multidimensional Networks

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models for multidimensional network data, where different levels of heterogeneity within and between networks can be considered. The proposed framework is developed in the family of latent space models, and it aims to distinguish symmetric relations between the nodes and node-specific features. Model parameters are estimated via a Markov Chain Monte Carlo algorithm. Simulated data and an application to a real example, on fruits import/export data, are used to illustrate and comment on the performance of the proposed models

Multilayer Networks

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 of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Spreading processes in Multilayer Networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.Comment: 21 pages, 3 figures, 4 table