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We present derivations of the contagion condition for a range of spreadingmechanisms on families of generalized random networks and bipartite randomnetworks. We show how the contagion condition can be broken into threeelements, two structural in nature, and the third a meshing of the contagionprocess and the network. The contagion conditions we obtain reflect thespreading dynamics in a clear, interpretable way. For threshold contagion, wediscuss results for all-to-all and random network versions of the model, anddraw connections between them.

A simple person's approach to understanding the contagion condition for spreading processes on generalized random networks