Entropic Centrality for non-atomic Flow Networks

Abstract

Given a graph, the notion of entropic centrality was introduced by Tutzauer to characterize vertices which are important in the sense that there is a high uncertainty about the destination of an atomic flow starting at them, assuming that at each hop, the flow is equally likely to continue to any unvisited vertex, or to be terminated there. We generalize this notion of entropic centrality to non-atomic flows, and furthermore show that the case of a non-atomic flow splitting with equal probability across different subsets of edges results in the same entropic centrality as that of the atomic flow. This gives a new and more generalized interpretation to the original entropic centrality notion. Finally, we demonstrate using network graphs derived from Bitcoin transactions that depending on the graph characteristics, the presented entropy based centrality metric can provide a unique perspective not captured by other existing centrality measures - particularly in identifying vertices with relatively low out-degrees which may nevertheless be connected to hub vertices, and thus can have high spread in the network.