New models for multi-class networks

• Published in: Journal of computational and applied mathematics 2021-10, Vol.394, p.113567, Article 113567
• Main Authors: De la Cruz Cabrera, Omar, Jin, Jiafeng, Reichel, Lothar
• Format: Article
• Language: English
• Subjects: Multi-class network; Network analysis
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2021.113567

Many complex phenomena can be modeled by networks, that is, by a set of nodes connected by edges. Networks are represented by graphs, and several algebraic and analytical methods have been developed for their study. However, in order to obtain a more useful representation of a system, it is often appropriate to include more information about the nodes and/or edges, and those additions make it necessary to adapt or modify such methods of study. Multi-class networks, in which the set of nodes and/or the set of edges are partitioned in two or more classes, are useful when different nodes and edges can play fundamentally distinct roles in the system. In this article we introduce new models and methods for multi-class networks, based on how the adjacency matrix is formed. We apply this approach to obtain measures of node importance or centrality, in particular using the Perron eigenvector. Perturbation results shed light on how the relative importance of a node changes by the addition of a single edge, and experiments with both synthetic and real data sets illustrate features of the methods discussed.