Process-Driven Betweenness Centrality Measures

Abstract

In network analysis, it is often desired to determine the most central node of a network, for example, for identifying the most influential individual in a social network. Borgatti states that almost all centrality measures assume that there exists a process moving through the network from node to node (Borgatti, Soc Netw 27(1):55–71, 2005). A node is then considered as central if it is important with respect to the underlying process. One often used measure is the betweenness centrality which is supposed to measure to which extent a node is “between” all other nodes by counting on how many shortest paths a node lies. However, most centrality indices make implicit assumptions about the underlying process. However, data containing a network and trajectories that a process takes on this network are available: this can be used for computing the centrality. Hence, in this work, we use existing data sets, human paths through the Wikipedia network, human solutions of a game in the game’s state space, and passengers’ travels between US American airports, in order to (1) test the assumptions of the betweenness centrality for these processes, and (2) derive several variants of a “process-driven betweenness centrality” using information about the network process. The comparison of the resulting node rankings yields that there are nodes which are stable with respect to their ranking while others increase or decrease in importance dramatically.