Weighted node degree centrality for hypergraphs

Many real-world social interactions involve multiple people, for e.g., authors collaborating on a paper, email exchanges made in a company and task-oriented teams in workforce. Simple graph representation of these activities destroys the group structure present in them. Hypergraphs have recently emerged as a better tool for modeling group interactions. However, methods in social hypernetwork analysis haven't kept pace. In this work, we extend the concept of node degree centrality to hypergraphs. We validate our proposed measures using alternate measures of influence available to us using two datasets namely, the DBLP dataset of scientific collaborations and the group network in a popular Chinese multi-player online game called CR3. We discuss several schemes for assigning weights to hyperedges and compare them empirically. Finally, we define separate weak and strong tie node degree centralities which improves performance of our models. Weak tie degree centrality is found to be a better predictor of influence in hypergraphs than strong tie degree centrality.