In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal-or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type centralities. In addition, we rigorously show that, under reasonable conditions, such centrality measures exist and are unique. Computer experiments and simulations demonstrate that the proposed measures provide substantially different results when applied to the same multiplex structure, and highlight the non-trivial relationships between the different measures of centrality introduced

The evolutionary dynamics of the Public Goods game addresses the emergence of cooperation within groups of individuals. However, the Public Goods game on large populations of interconnected individuals has been usually modeled without any knowledge about their group structure. In this paper, by focusing on collaboration networks, we show that it is possible to include the mesoscopic information about the structure of the real groups by means of a bipartite graph. We compare the results with the projected (coauthor) and the original bipartite graphs and show that cooperation is enhanced by the mesoscopic structure contained. We conclude by analyzing the influence of the size of the groups in the evolutionary success of cooperation.Evolutionary game dynamics on graphs has become a hot topic of research during the last years. The attention has been mainly focused on 2-players games, such as the Prisoner's Dilemma game, since the pairwise interactions can be easily implemented on top of networked substrates. However, for m-players game, such as the Public Goods game, the microscopic description about the pairwise interactions contained in the network is not enough, since m-players game are intrinsically defined at the mesoscopic network level. This mesoscopic level describes how individuals engage into groups where the Public Goods games are played. However, the actual group structure of networks has not been considered in the literature, being automatically substituted by a fictitious one. In this work, we study the emergence of cooperation in collaboration networks, by incorporating the real group structure to the evolutionary dynamics of the Public Goods game. Our results are compared with those obtained when the mesoscopic structure is ignored. We show that cooperation is actually enhanced when the group structure is taken into account, thus providing a novel structural mechanism, relying on the mesoscale level of large social systems, that promotes cooperation. Moreover, we further show that the particular characteristics of the group structure strongly influence the survival of cooperation.