C:\Papers\Probabilistic Information Flow\Centrality and Network Flow 3c.doc Centrality and Network Flow

Centrality measures, or at least popular interpretations of these measures, make implicit assumptions about the manner in which traffic flows 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 that 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 traffic flows, and that this provides a new and useful way of thinking about centrality. ♣ This paper was first presented at the Sunbelt International Social Networks Conference 2002, in New Orleans. It was subsequently presented at the Complexity colloquium series at Harvard University, in April, 2002, and at the Institute for Mathematics and its Applications (IMA) in Minneapolis, in November, 2003. I am grateful to Mark Newman for help and encouragement, along with Phil Bonacich and Martin Everett. This research was supported by Office of Naval Research grant number N000140211032.