Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems elements. These networks have attracted a lot of attention recently because their
study allows considering different dynamical modes concurrently. Here, we revise the main concepts and tools developed up to date. Specifically, we focus on several metrics for multilayer network characterization as well as on the spectral properties of the system, which ultimately enable for the dynamical characterization of several critical phenomena. The theoretical framework is also applied for description of real-world multilayer systems.
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open problem. From B
iology to Sociology and Economy, the identification of false and missing positives has become a problem that calls for a solution. In this work we extend one of newest, best performing models -due to Guimera and Sales-Pardo in 2009- to directed networks. The new methodology is able to identify missing and spurious directed interactions, which renders it particularly useful to analyze data reliability in systems like trophic webs, gene regulatory networks, communication patterns and social systems. We also show, using real-world networks, how the method can be employed to help searching for new interactions in an efficient way.
