Clustering Misclassification Error. A clustering experiment using metrics and non-metrics (y-axis) for different clustering parameters (x-axis). We sample graphs with n=50 nodes from the six classes, shown in Table 3. We compute distances between them using nine different algorithms from Table 2. Only the distances in our family (DSL1, DSL2, ORTHOP, and ORTHFR) are metrics. The resulting graphs are clustered using hierarchical agglomerative clustering (Hartigan 1975) using Average, Centroid, Complete, Median, Single, Ward, Weighted as a means of merging clusters. Colors represent the fraction of misclassified graphs, with the minimal misclassification rate per distance labeled explicitly. Metrics outperform other distance scores across all clustering methods. The error rate of a random guess is ≈0.8.