Abstract
The notion of entropic centrality measures how central a node is in terms of how uncertain the destination of a flow starting at this node is: the more uncertain the destination, the more well connected and thus central the node is deemed. This implicitly assumes that the flow is indivisible, and at every node, the flow is transferred from one edge to another. The contribution of this paper is to propose a split-and-transfer flow model for entropic centrality, where at every node, the flow can actually be arbitrarily split across choices of neighbours. We show how to map this to an equivalent transfer entropic centrality set-up for the ease of computation, and carry out three case studies (an airport network, a cross-shareholding network and a Bitcoin transactions subnetwork) to illustrate the interpretation and insights linked to this new notion of centrality.
Highlights
Centrality is a classical measure used in graph theory and network analysis to identify important vertices
This is the idea behind eigenvector centrality discussed by Newman (2009), which was already debated by Bonacich (1972), who later generalized it to alpha centrality (Bonacich & Lloyd, 2001)
We studied the concept of entropic centrality proposed by Tutzauer (2007), which originally determined the importance of a vertex based on the extent of dissemination of an indivisible flow originating at it, by considering the uncertainty in determining its destination
Summary
Centrality is a classical measure used in graph theory and network analysis to identify important vertices. Using Katz’s intuition, eigenvector based centralities count possible unconstrained walks, and they are consistent with a scenario where every vertex influences all of its neighbors simultaneously, which is consistent with parallel deduplication This flow characterization is of interest for this work, since we will be looking at a case where a flow is not just transferred, and split among outgoing edges, with the possibility to partly remain at any node it encounters. For a given node u, we compute the expected flow from u to a chosen neighbor v Every such choice of x comes with a probability q(x), and every edge (u,v) in x has a weight ωx (u,v), which sums up to fuv = q(x)ωx (u,v),.
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