  We report on an exceptionally accurate spin-glass-type Potts model for
community detection. With a simple algorithm, we find that our approach is at
least as accurate as the best currently available algorithms and robust to the
effects of noise. It is also competitive with the best currently available
algorithms in terms of speed and size of solvable systems. We find that the
computational demand often exhibits superlinear scaling L^1.3 where L is the
number of edges in the system, and we have applied the algorithm to synthetic
systems as large as 40x10^6 nodes and over 1x10^9 edges. A previous stumbling
block encountered by popular community detection methods is the so-called
"resolution limit." Being a "local" measure of community structure, our Potts
model is free from this resolution-limit effect, and it further remains a local
measure on weighted and directed graphs. We also address the mitigation of
resolution-limit effects for two other popular Potts models.
