Attachment Centrality for Weighted Graphs

Measuring how central nodes are in terms of connecting a network has recently received increasing attention in the literature and a few dedicated centrality measures have been proposed. One of them is the Attachment Centrality that is the only one that satisfies certain natural axioms desirable for connectivity, such as Myerson's Fairness, Monotonicity, Locality and Normalization. Unfortunately, the Attachment Centrality is defined only for unweighted graphs which makes this measure ill-fitted for various applications. For instance, covert networks are typically weighted, where the weights carry additional intelligence available about criminals or terrorists and the links between them. To analyse such settings, we extend the Attachment Centrality to weighted graphs and show that it is closely related to the Degree Centrality by an axiomatic analysis.