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Notions of community quality underlie network clustering. While studiessurrounding network clustering are increasingly common, a precise understandingof the realtionship between different cluster quality metrics is unknown. Inthis paper, we examine the relationship between stand-alone cluster qualitymetrics and information recovery metrics through a rigorous analysis of fourwidely-used network clustering algorithms -- Louvain, Infomap, labelpropagation, and smart local moving. We consider the stand-alone qualitymetrics of modularity, conductance, and coverage, and we consider theinformation recovery metrics of adjusted Rand score, normalized mutualinformation, and a variant of normalized mutual information used in previouswork. Our study includes both synthetic graphs and empirical data sets of sizesvarying from 1,000 to 1,000,000 nodes.  We find significant differences among the results of the different clusterquality metrics. For example, clustering algorithms can return a value of 0.4out of 1 on modularity but score 0 out of 1 on information recovery. We findconductance, though imperfect, to be the stand-alone quality metric that bestindicates performance on information recovery metrics. Our study shows that thevariant of normalized mutual information used in previous work cannot beassumed to differ only slightly from traditional normalized mutual information.  Smart local moving is the best performing algorithm in our study, butdiscrepancies between cluster evaluation metrics prevent us from declaring itabsolutely superior. Louvain performed better than Infomap in nearly all thetests in our study, contradicting the results of previous work in which Infomapwas superior to Louvain. We find that although label propagation performspoorly when clusters are less clearly defined, it scales efficiently andaccurately to large graphs with well-defined clusters.

Analysis of Network Clustering Algorithms and Cluster Quality Metrics at Scale