Betweenness centrality based on a new definition of shortest path in directed hypergraphs

Abstract

Hyperedges that can provide connections from sets of nodes to other sets of nodes are not defined in standard directed graphs. Thus, existing algorithms for directed graphs cannot be used to directed hypergraphs. This paper proposes an algorithm for betweenness centrality in directed hypergraphs. We first define a path and the shortest path between two nodes because existing definition of a path cannot give all the required information to traverse in directed hypergraphs. And then provide a betweenness centrality computation algorithm for nodes and hyperedges seperately. We also show through experiments that the betweenness centrality based on the concepts of the path and shortest paths in the directed hypergraphs proposed in this paper is a measure better suited in practice than betweenness centrality of the reduction graph of given hypergraphs.