  We present a novel approach to partitioning network nodes into
non-overlapping communities - a key step in revealing network modularity and
hierarchical organization. Our methodology, applicable to networks with both
weighted and unweighted symmetric edges, uses random walks to explore
neighboring nodes in the same community. The walk-likelihood algorithm (WLA)
produces an optimal partition of network nodes into a given number of
communities. The walk-likelihood community finder (WLCF) employs WLA to predict
both the optimal number of communities and the corresponding network partition.
We have extensively benchmarked both algorithms, finding that they outperform
or match other methods in terms of the modularity of predicted partitions and
the number of links between communities. Making use of the computational
efficiency of our approach, we investigated a large-scale map of roads and
intersections in the state of Colorado. Our clustering yielded geographically
sensible boundaries between neighboring communities.
