Information transmission likelihood between two arbitary vertices of a graph as a function of graph density in a social graph

Suppose a social graph is represented as as an abstract data structure of a graph where bi-directional information flow is possible through the edges of the graph. I am interested in evaluating the probability that information generated at a given node or vertex is received at some other arbitrary node in the graph. (say P{n1}{n2} )

Given the graph density(average number of edges per vertex) (say D) Assuming a constant probability of it getting past its f开发者_C百科irst neighbors. (say p)

An algorithm/simulation setup for this would be equally helpful.