Random walk can be applied to any network?

Question

[Yoomi]

We are using the random walk algorithm to the biology network for community detection. In the thesis, there is the condition to apply the random walks in the graph. It says that "The graph G is connected and primitive (the gcd of the cycle lengths of G is 1, due to the loops on each vertex)". But our biology graph is sparse and not all vertex is connected.

So the question is that it is possible to apply the random walk algorithm in the sparse and disconnected networks?