  Identifying strongly connected substructures in large networks provides
insight into their coarse-grained organization. Several approaches based on the
optimization of a quality function, e.g., the modularity, have been proposed.
We present here a multistep extension of the greedy algorithm (MSG) that allows
the merging of more than one pair of communities at each iteration step. The
essential idea is to prevent the premature condensation into few large
communities. Upon convergence of the MSG a simple refinement procedure called
"vertex mover" (VM) is used for reassigning vertices to neighboring communities
to improve the final modularity value. With an appropriate choice of the step
width, the combined MSG-VM algorithm is able to find solutions of higher
modularity than those reported previously. The multistep extension does not
alter the scaling of computational cost of the greedy algorithm.
