Visualization and Extraction of Important Structural Changes via Dynamic Hypergraph Embedding

Abstract

Some real-world networks have structures that change dynamically over time. These changes include the addition or deletion of nodes and edges, and the rewiring of edges. Even when edge rewiring occurs, the degree of impact tends to vary depending on the location where it occurs and the nature of the node. In this study, we propose an embedding method that makes it easy to visually capture structural changes in dynamic hypergraphs. Furthermore, by quantifying the degree of influence of each hypernode, we attempt to extract influential structural changes that alter the location of many nodes in the network. Specifically, the positions of nodes are calculated by an embedding method that embeds hypernodes and hyperedges into the unit hypersphere based on their adjacencies, and the degree of influence on the nodes is calculated by the angle of the embedding vectors before and after the structural change occurs. We then propose a measure which is the average value of the influence degree of all nodes. Based on experimental evaluation using several synthetic datasets, we confirmed that our proposed measure quantifies the important structural changes as larger scores, conversely trivial changes as smaller ones.