Centrality in valued graphs: A measure of betweenness based on network flow

A new measure of centrality, C F, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman's original measure, C B, the new measure differs from the original in two important ways. First, C F is defined for both valued and non-valued graphs. This makes C F applicable to a wider variety of network datasets. Second, the computation of C F is not based on geodesic paths as is C B but on all the independent paths between all pairs of points in the network.