Large Structures Seminar: Mikko Kivelä

Network science has been very successful in investigations of a wide variety of applications from biology and the social sciences to physics, technology, and more. In many situations, it is already insightful to use a simple (and typically naive) representation as a simple, binary graph in which nodes are entities and unweighted edges encapsulate the interactions between those entities. This allows one to use the powerful methods and concepts for example from graph theory, and numerous advances have been made in this way. However, as network science has matured and (especially) as ever more complicated data has become available, it has become increasingly important to develop tools to analyse more complicated structures. For example, many systems that were typically initially studied as simple graphs are now often represented as time-dependent networks, networks with multiple types of connections, or interdependent networks. This has allowed deeper and more realistic analyses of complex networked systems, but it has simultaneously introduced mathematical constructions, jargon, and methodology that are specific to research in each type of system. Recently, the concept of “multilayer networks” was developed in order to unify the aforementioned disparate language (and disparate notation) and to bring together the different generalised network concepts that included layered graphical structures. In this talk, I will introduce multilayer networks and discuss how to study their structure. Generalisations of the clustering coefficient for multiplex networks and graph isomorphism for general multilayer networks are used as illustrative examples.