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Order the vertices of a directed random graph \math{v_1,...,v_n}; edge\math{(v_i,v_j)} for \math{i<j} exists independently with probability \math{p}.This random graph model is related to certain spreading processes on networks.We consider the component reachable from \math{v_1} and prove existence of asharp threshold \math{p^*=\log n/n} at which this reachable componenttransitions from \math{o(n)} to \math{\Omega(n)}.

Spreading Processes and Large Components in Ordered, Directed Random Graphs