On MultiAspect Graphs

Abstract

Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to represent time-varying networks. We introduce the concept of MultiAspect Graph (MAG) as a graph generalization that we prove to be isomorphic to a directed graph, and also capable of representing all these previous generalizations. In our proposal, the set of vertices, layers, time instants, or any other independent feature is considered as an aspect of the MAG. For instance, a MAG is able to represent multilayer or time-varying networks, while both concepts can also be combined to represent a multilayer time-varying network. Since the MAG structure admits an arbitrary (finite) number of aspects, it hence introduces a powerful modelling abstraction for networked complex systems. This paper formalizes the concept of MAG and then derives theoretical results that can be useful in the analysis of complex networked systems modelled using the proposed MAG abstraction.