Flowthrough Centrality: A Stable Node Centrality Measure

This paper introduces flowthrough centrality, a node centrality measure determined from the hierarchical maximum concurrent flow problem (HMCFP). Based upon the extent to which a node is acting as a hub within a network, this centrality measure is defined to be the fraction of the flow passing through the node to the total flow capacity of the node. Flowthrough centrality is compared to the commonly-used centralities of closeness centrality, betweenness centrality, and flow betweenness centrality, as well as to stable betweenness centrality to measure the stability (i.e., accuracy) of the centralities when knowledge of the network topology is incomplete or in transition. Perturbations do not alter the flowthrough centrality values of nodes that are based upon flow as much as they do other types of centrality values that are based upon geodesics. The flowthrough centrality measure overcomes the problem of overstating or understating the roles that significant actors play in social networks. The flowthrough centrality is canonical in that it is determined from a natural, realized flow universally applicable to all networks.