Dithering and betweenness centrality in weighted graphs

This paper applies dithering to design a node centrality measure for weighted graphs. The construction is an improvement on the stable betweenness centrality measure which, in turn, was introduced as a robust alternative to the well-known betweenness centrality. We interpret any given graph as the mean representation of a distribution of graphs and define the dithered centrality value as the expected centrality value across all graphs in the distribution. We show that the dithered stable betweenness centrality measure preserves robustness in the presence of noise while improving the behavior of stable betweenness. Numerical experiments demonstrate the advantages of dithering by comparing the performance of betweenness, stable betweenness and dithered stable betweenness centralities in terms of robustness to noise, dependence on the number and quality of alternative paths, and distribution of centrality values across the graph.