Centrality and network flow

Abstract

Centrality measures, or at least our interpretations of these measures, make implicit assumptions about the manner in which things flow through a network. For example, some measures count only geodesic paths, apparently assuming that whatever flows through the network only moves along the shortest possible paths. This paper lays out a typology of network flows based on two dimensions of variation, namely, the kinds of trajectories that traffic may follow (geodesics, paths, trails or walks), and the method of spread (broadcast, serial replication, or transfer). Measures of centrality are then matched to the kinds of flows they are appropriate for. Simulations are used to examine the relationship between type of flow and the differential importance of nodes with respect to key measurements such as speed of reception of traffic and frequency of receiving traffic. It is shown that the off-the-shelf formulas for centrality measures are fully applicable only for the specific flow processes they are designed for, and that when they are applied to other flow processes they get the “wrong” answer. It is noted that the most commonly used centrality measures are not appropriate for most of the flows we are routinely interested in. A key claim made in this paper is that centrality measures can be regarded as generating expected values for certain kinds of node outcomes (such as speed and frequency of reception) given implicit models of how things flow.