On decay centrality

We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness centrality. We show that for low values of the decay parameter the nodes with maximum decay centrality also have maximum degree, whereas for high values of the decay parameter they also maximize closeness. For intermediate values of the decay parameter, we perform an extensive set of simulations on random networks and find that maximum degree or closeness are good proxies for maximum decay centrality. In particular, in the vast majority of simulated networks, the nodes with maximum decay centrality are characterized by a threshold on the decay parameter below which they belong to the set of nodes with maximum degree and above which they belong to the set of nodes with maximum closeness. The threshold values vary with the characteristics of the network. Moreover, nodes with maximum degree or closeness are highly ranked in terms of decay centrality even when they are not maximizing it. The latter analysis allows us to propose a simple rule of thumb that ensures a nearly optimal choice with very high probability.