  Random walks on simple graphs in connection with electrical resistor networks
lead to the definition of Markov chains with transition probability matrix in
terms of electrical conductances. We extend this definition to an effective
transition matrix $P_{ij}$ to account for the probability of going from vertex
$i$ to any vertex $j$ of the original connected graph $G$. Also, we present an
algorithm based on the definition of this effective transition matrix among
vertices in the network to extract a topological feature related to the manner
graph $G$ has been organized. This topological feature corresponds to the
communities in the graph.
