  This paper introduces two new closely related betweenness centrality measures
based on the Randomized Shortest Paths (RSP) framework, which fill a gap
between traditional network centrality measures based on shortest paths and
more recent methods considering random walks or current flows. The framework
defines Boltzmann probability distributions over paths of the network which
focus on the shortest paths, but also take into account longer paths depending
on an inverse temperature parameter. RSP's have previously proven to be useful
in defining distance measures on networks. In this work we study their utility
in quantifying the importance of the nodes of a network. The proposed RSP
betweenness centralities combine, in an optimal way, the ideas of using the
shortest and purely random paths for analysing the roles of network nodes,
avoiding issues involving these two paradigms. We present the derivations of
these measures and how they can be computed in an efficient way. In addition,
we show with real world examples the potential of the RSP betweenness
centralities in identifying interesting nodes of a network that more
traditional methods might fail to notice.
