Spreading Processes and Large Components in Ordered, Directed Random Graphs
Abstract
Order the vertices of a directed random graph v1,...,vn; edge (vi,vj) for i<j exists independently with probability p. This random graph model is related to certain spreading processes on networks. We consider the component reachable from v1 and prove existence of a sharp threshold p*= n/n at which this reachable component transitions from o(n) to (n).
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