Empirical comparative study of similarity indexes in scientometrics co-authorship analysis

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Similarity indexes are widely used in the field of scientometrics either in co-words, co-citations, bibliographic coupling, or co-authorship, and very recently in link prediction and system recommender. Despite the rich literature on the comparison of various indexes very rarely a consensus is being reached on the appropriateness of a specific one. This paper aims to enhance empirical understanding of similarity indexes within the context of co-authorship networks, which are widely used and highly relevant in scientometrics. The objective is to assist scientometricians in better analyzing co-authorship networks and selecting the most suitable similarity index for their studies. The research examines two types of co-authorship networks - one with low density at the individual level and another with high density at the country level - using five commonly applied similarity indexes: Jaccard, Salton, Dice-Sorenson, Pearson, and Association Strength. The study confirms that, as theoretically expected, the Salton index follows a concave increasing function of the Jaccard index, with Jaccard values consistently lower, regardless of network density. The concave shape of the curve is more pronounced in the case of low dense network. A linear function is found between Dice-Sorenson and Salton. Additionally, Pearson is observed to be 'orthogonal' to Jaccard, Salton, and Dice-Sorenson, indicating a lack of direct correlation. In contrast, Association Strength behaves differently: in a high-density network, it is 'orthogonal' to Jaccard, Salton, and Dice-Sorenson and shows no correlation with Pearson. However, in a low-density network, Association Strength displays the opposite behavior.