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Similarity index measures the topological proximity of node pairs in acomplex network. Numerous similarity indices have been defined andinvestigated, but the dependency of structure on the performance of similarityindices has not been sufficiently investigated. In this study, we investigatedthe relationship between the performance of similarity indices and structuralproperties of a network by employing a two-state random network. A node in atwo-state network has binary types that are initially given, and a connectionprobability is determined from the state of the node pair. The performance ofsimilarity indices affects the number of links and the ratio ofintra-connections to inter-connections. Similarity indices have differentcharacteristics depending on their type. Local indices perform well insmall-size networks and do not depend on whether the structure isintra-dominant or inter-dominant. In contrast, global indices perform better inlarge-size networks, and some such indices do not perform well in aninter-dominant structure. We also found that link prediction performance andthe performance of similarity are correlated in both model networks andempirical networks. This relationship implies that link prediction performancecan be used as an approximation for the performance of the similarity indexwhen metadata for node types are unavailable. This relationship may help tofind the appropriate index for given networks.

A study on the performance of similarity indices and its relationship with link prediction: a two-state random network case