  In this paper we elaborate upon a measure of node influence in social
networks, which was recently proposed by Vassio et al., IEEE Trans. Control
Netw. Syst., 2014. This measure quantifies the ability of the node to sway the
average opinion of the network. Following the approach by Vassio et al., we
describe and study a distributed message passing algorithm that aims to compute
the nodes' influence. The algorithm is inspired by an analogy between
potentials in electrical networks and opinions in social networks. If the graph
is a tree, then the algorithm computes the nodes' influence in a number of
steps equal to the diameter of the graph. On general graphs, the algorithm
converges asymptotically to a meaningful approximation of the nodes' influence.
In this paper we detail the proof of convergence, which greatly extends
previous results in the literature, and we provide simulations that illustrate
the usefulness of the returned approximation.
