Multiaspect graphs

• Ano de defesa: 2016
• Autor(a) principal: Wehmuth, Klaus
• Orientador(a): Ziviani, Artur
• Banca de defesa: Szwarcfiter, Jayme Luiz , Albuquerque, Célio Vinicius Neves de , Menasché, Daniel Sadoc, Gomes, Antônio Tadeu Azevedo, Vieira, Paulo César Marques
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Laboratório Nacional de Computação Científica
• Programa de Pós-Graduação: Programa de Pós-Graduação em Modelagem Computacional
• Departamento: Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA)
• País: Brasil
• Palavras-chave em Português: Teoria dos grafos; Generalização de grafos; Redes multicamada; Graphs theory; Graphs generalization
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO::MATEMATICA SIMBOLICA
• Link de acesso: https://tede.lncc.br/handle/tede/244

Different graph generalizations have been recently used in an ad hoc manner to represent time-varying complex networks, i.e. networks in which vertices and edges may vary in time. Similar constructions have also been used to represent multilayer networks, i.e. systems formed by distinct interdependent layers where each layer can be seen as a complex network. In this thesis, we introduce the concept of MultiAspect Graph (MAG). We show that a MAG is isomorphic to a directed graph, which is an important theoretical result because this allows the use of the isomorphic directed graph as a tool to analyze both the properties of a MAG and the behavior of dynamic processes over a MAG. In our proposal, the set of vertices, layers, time instants, or any other independent feature of the system being modelled 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. Further, we present algebraic representations and basic algorithms for MAGs, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Building upon the basic MAG concept, we also present derived applications, such as a MAG-based unifying model for time-varying graphs as well as MAG-based centrality notions.