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Correlations for paths in random orientations of G(n,p) and G(n,m)

Correlations for paths in random orientations of G(n,p) and G(n,m)

Abstract We study random graphs, both G( n,p) and G( n,m), with random orientations on the edges. For three fixed distinct vertices s,a,b we study the correlation, in the combine probability space, of the events $\{a\to s\}$ and $\{s\to b\}$ . For G(n,p) , we prove that there is a …