Title: Generalization of Effective Conductance Centrality for Egonetworks,
Abstract: We study the popular centrality measure known as effective conductance or in
some circles as information centrality. This is an important notion of
centrality for undirected networks, with many applications, e.g., for random
walks, electrical resistor networks, epidemic spreading, etc. In this paper, we
first reinterpret this measure in terms of modulus (energy) of families of
walks on the network. This modulus centrality measure coincides with the
effective conductance measure on simple undirected networks, and extends it to
much more general situations, e.g., directed networks as well. Secondly, we
study a variation of this modulus approach in the egocentric network paradigm.
Egonetworks are networks formed around a focal node (ego) with a specific order
of neighborhoods. We propose efficient analytical and approximate methods for
computing these measures on both undirected and directed networks. Finally, we
describe a simple method inspired by the modulus point-of-view, called shell
degree, which proved to be a useful tool for network science.