  Notions of community quality underlie network clustering. While studies
surrounding network clustering are increasingly common, a precise understanding
of the realtionship between different cluster quality metrics is unknown. In
this paper, we examine the relationship between stand-alone cluster quality
metrics and information recovery metrics through a rigorous analysis of four
widely-used network clustering algorithms -- Louvain, Infomap, label
propagation, and smart local moving. We consider the stand-alone quality
metrics of modularity, conductance, and coverage, and we consider the
information recovery metrics of adjusted Rand score, normalized mutual
information, and a variant of normalized mutual information used in previous
work. Our study includes both synthetic graphs and empirical data sets of sizes
varying from 1,000 to 1,000,000 nodes.
  We find significant differences among the results of the different cluster
quality metrics. For example, clustering algorithms can return a value of 0.4
out of 1 on modularity but score 0 out of 1 on information recovery. We find
conductance, though imperfect, to be the stand-alone quality metric that best
indicates performance on information recovery metrics. Our study shows that the
variant of normalized mutual information used in previous work cannot be
assumed to differ only slightly from traditional normalized mutual information.
  Smart local moving is the best performing algorithm in our study, but
discrepancies between cluster evaluation metrics prevent us from declaring it
absolutely superior. Louvain performed better than Infomap in nearly all the
tests in our study, contradicting the results of previous work in which Infomap
was superior to Louvain. We find that although label propagation performs
poorly when clusters are less clearly defined, it scales efficiently and
accurately to large graphs with well-defined clusters.
