Abstract
Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of approaches to compare layers in multiplex networks. Our taxonomy includes, systematizes and extends existing approaches, and is complemented by a set of practical guidelines on how to apply them.
Highlights
Multiplex networks provide a simple yet expressive way to model a wide range of physical and social systems as sets of entities connected by multiple types of relationships, that in this paper we call layers following the terminology in [1]
We known from previous research that the relationships between layers have an impact on dynamic processes such as behaviour and information diffusion [2]
While the problem of comparing different networks has been thoroughly investigated in the literature [5,6,7,8,9,10,11,12,13], the problem of quantifying layer similarity where the same nodes can be present in multiple layers has not been studied in a systematic and comprehensive way so far
Summary
Multiplex networks provide a simple yet expressive way to model a wide range of physical and social systems as sets of entities connected by multiple types of relationships, that in this paper we call layers following the terminology in [1]. The adjacency matrices for our working example are shown in figure 2 This representation is not the most appropriate to define similarity measures, for two main reasons. It is incomplete, because it only allows representing node-aligned multiplex networks. Each cell ps,c of a property matrix contains the value of the function describing the structure s (for example, a node) on layer c, and different observational functions can be used to define different types of similarity. Property matrices provide a more general and informative representation of multiplex networks than adjacency matrices—which are still useful when the objective is just to know about the edges in a node-aligned network. The terminology and notation used in the paper is summarized in table 1
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