  We study the asymptotic behaviour of Markov processes on large weighted
Erdos-Renyi graphs where the transition rates of the vertices are only
influenced by the state of their neighbours and the corresponding weight on the
edges. We find the ratio of vertices being in a certain state will converge to
the solution of a differential equation obtained from mean field approximation
if the graph is dense enough, namely, the average degree is at least of order
$N^{\frac{1}{2}+\epsilon}$. Proof for convergence in probability in the
transient regime is shown.
