On MultiAspect Graphs

TL;DR

This paper introduces MultiAspect Graphs (MAGs), a unified framework capable of representing complex multilayer, time-varying, and higher-order networks, and proves their isomorphism to directed graphs.

Contribution

The paper formalizes MAGs as a general graph model that unifies various network representations and proves their theoretical properties, expanding modeling capabilities.

Findings

MAGs are isomorphic to directed graphs.

MAGs can represent multilayer and time-varying networks.

Theoretical results facilitate analysis of complex networked systems.

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 previous generalizations. In our proposal, the set of vertices, layers, time instants, or any other independent features are 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 and even other higher-order networks. 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 derives theoretical results useful in the analysis of complex networked systems modelled using the proposed MAG abstraction. We also present an overview of the MAG applicability.