title: Mean size of avalanches on directed random networks with arbitrary degree distributions.
abstract: The mean size of unordered binary avalanches on infinite directed random networks may be determined using the damage propagation function introduced by [B. Samuelsson and J. E. S. Socolar, Phys. Rev. E 74, 036113 (2006)]. The derivation of Samuelsson and Socolar explicitly assumes a Poisson distribution of out-degrees. It is shown here that the damage propagation function method may be used whenever the in-degree and out-degree of network nodes are independently distributed; in particular, it is not necessary that the out-degree distribution be Poisson. The general case of correlated in- and out-degrees is discussed and numerical simulations (on large finite networks) are compared with the theoretical predictions (for infinite networks).
authors.affiliation: Department of Mathematics & Statistics, University of Limerick, Ireland.
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson