  The harmonic influence is a measure of the importance of nodes in social
networks, which can be approximately computed by a distributed message-passing
algorithm. In this extended abstract we look at two open questions about this
algorithm. How does it perform on real social networks, which have complex
topologies structured in communities? How does it perform when the network
topology changes while the algorithm is running? We answer these two questions
by numerical experiments on a Facebook ego network and on synthetic networks,
respectively. We find out that communities can introduce artefacts in the final
approximation and cause the algorithm to overestimate the importance of "local
leaders" within communities. We also observe that the algorithm is able to
adapt smoothly to changes in the topology.
