Abstract
Many real-world complex systems can be described by a network structure, where a set of elementary units, e.g, human, gene, sensor, or other types of 'nodes' are connected by edges that represent dyadic relations, e.g., an observed interaction or an inferred dependence measured by correlation or mutual information. Such so-called relevance networks can be undirected or directed graphs depending on whether the relevance measure is symmetric or asymmetric. Often there are multiple ways that pairs of nodes might be related, e.g., by family ties, friendships, and professional connections in a social network. A multi-layer relevance network can be used to simultaneously capture these different types of relations. Dynamic relevance networks whose edges change over time are a type of multi-layer network, with each layer representing relations at a particular time instant. In this paper, we review and discuss multi-layer relevance network models in the context of relevance measures and node centrality for datasets with multivalent relations. We illustrate these models for dynamic gene regulatory networks and dynamic social networks.