Spreading Processes and Large Components in Ordered, Directed Random Graphs
Combinatorics
2012-09-12 v2 Discrete Mathematics
Social and Information Networks
Abstract
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 a sharp threshold \math{p^*=\log n/n} at which this reachable component transitions from \math{o(n)} to \math{\Omega(n)}.
Cite
@article{arxiv.1209.2088,
title = {Spreading Processes and Large Components in Ordered, Directed Random Graphs},
author = {Paul Horn and Malik Magdon-Ismail},
journal= {arXiv preprint arXiv:1209.2088},
year = {2012}
}
Comments
Working paper, under review