The probabilities of node-to-node diffusion in fixed networks

Network transmission of infection or information can have serious social, economic and political effects. Heuristics are often used to address the computationally hard optimal seeding problem, and to approximate SIR models of epidemics. This paper develops a new heuristic for the probabilities of node-to-node diffusion in networks. The simple formula uses De Morgan’s laws to eliminate the double counting of signals found in diffusion centrality. It provides a new measure of centrality — word-of-mouth centrality — which gives the average probability that a signal emitted by a node will be received by other nodes in the network by diffusion. The paper also gives two further centrality measures for the cases when some nodes obstruct or conceal signals, called obstructed centrality and visibility centrality.