  We have found that known community identification algorithms produce
inconsistent communities when the node ordering changes at input. We propose
two metrics to quantify the level of consistency across multiple runs of an
algorithm: pairwise membership probability and consistency. Based on these two
metrics, we address the consistency problem without compromising the
modularity. Our solution uses pairwise membership probabilities as link weights
and generates consistent communities within six or fewer cycles. It offers a
new tool in the study of community structures and their evolutions.
