Topological metrics in academic genealogy graphs

Academic genealogy aims to structure and analyze the mentoring relationships between advisor and advisee. The representation of this structure results in academic genealogy graphs. For the analysis and characterization of these graphs, we present a set of metrics and their corresponding mirror metrics that capture the characteristics of its topological structure and represent them as quantitative attributes. The metrics of fecundity, fertility, descendants, cousins, generations, and relationships consider the descendants of the academics represented in the graph. The mirror metric of these topological metrics considers the ascendancy of academics. Individually, the metrics have strong semantic intuition and define characteristics regarding the performance in the mentoring of an academic. Together, the metrics are useful for the identification, characterization, and classification of communities and their members. The genealogical data available through the platforms of the Mathematics Genealogy Project and the Academic Family Tree were used as case studies. Two hundred thirteen thousand and 675,000 academic records were obtained for each project. We analyze the capacity of characterization of the metrics using the structuring of a similarity graph and through the distribution of the nodes in principal components. We observed that the set of metrics is capable of capturing the configuration pattern existing in genealogy graphs independently of its scale.