  Various kinds of spread of influence occur in real world social and virtual
networks. These phenomena are formulated by activation processes and
irreversible dynamic monopolies in combinatorial graphs representing the
topology of the networks. In most cases the nature of influence is weighted and
the spread of influence depends on the weight of edges. The ordinary
formulation and results for dynamic monopolies do not work for such models. In
this paper we present a graph theoretical analysis for spread of weighted
influence and mention a real world example realizing the activation model with
weighted influence. Then we obtain some extremal bounds and algorithmic results
for activation process and dynamic monopolies in directed and undirected graphs
with weighted edges.
