  Let G=(V,E) be an undirected loopless graph with possible parallel edges and
s and t be two vertices of G. Assume that vertex s is labelled at the initial
time step and that every labelled vertex copies its labelling to neighbouring
vertices along edges with one labelled endpoint independently with probability
p in one time step. In this paper, we establish the equivalence between the
expected s-t first arrival time of the above spread process and the notion of
the stochastic shortest s-t path. Moreover, we give a short discussion of
analytical results on special graphs including the complete graph and s-t
series-parallel graphs. Finally, we propose some lower bounds for the expected
s-t first arrival time.
