A framework for the construction of generative models for mesoscale structure in multilayer networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks

Interbank markets and multiplex networks: centrality measures and statistical null models

The interbank market is considered one of the most important channels of contagion. Its network representation, where banks and claims/obligations are represented by nodes and links (respectively), has received a lot of attention in the recent theoretical and empirical literature, for assessing systemic risk and identifying systematically important financial institutions. Different types of links, for example in terms of maturity and collateralization of the claim/obligation, can be established between financial institutions. Therefore a natural representation of the interbank structure which takes into account more features of the market, is a multiplex, where each layer is associated with a type of link. In this paper we review the empirical structure of the multiplex and the theoretical consequences of this representation. We also investigate the betweenness and eigenvector centrality of a bank in the network, comparing its centrality properties across different layers and with Maximum Entropy null models.Comment: To appear in the book "Interconnected Networks", A. Garas e F. Schweitzer (eds.), Springer Complexity Serie

Local Convergence and Global Diversity: The Robustness of Cultural Homophily

Recent extensions of the Axelrod model of cultural dissemination (Klemm et al 2003) showed that global diversity is extremely fragile with small amounts of cultural mutation. This seemed to undermine the original Axelrod theory that homophily preserves diversity. We show that cultural diversity is surprisingly robust if we increase the tendency towards homophily as follows. First, we raised the threshold of similarity below which influence is precluded. Second, we allowed agents to be influenced by all neighbors simultaneously, instead of only one neighbor as assumed in the orginal model. Computational experiments show how both modifications strongly increase the robustness of diversity against mutation. We also find that our extensions may reverse at least one of the main results of Axelrod. While Axelrod predicted that a larger number of cultural dimensions (features) reduces diversity, we find that more features may entail higher levels of diversity.Comment: 21 pages, 8 figures, Submitted for presentation in Mathematical Sociology Session, Annual Meeting of the American Sociological Association (ASA), 200

Interdisciplinary and physics challenges of Network Theory

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.Comment: (7 pages, 4 figures