Measuring the Similarity Between Trees of Different Order

Graphs encode relationships between data. However, due to their versatility, it is often difficult to generalize the notion of similarity between two graphs using a distance function. Since graphs can represent various data sets, specific distance metrics need to be tailored for questions we are interested in answering or the data set we are working with. This project is motivated by ongoing investigations into the evolution of female gender representation in mathematics. By building off previous work that has taken data from the Mathematics Genealogy Project and modeled this evolution of representation via a tree, we would like to develop a metric that compares different branches of a genealogy tree. The goal is to determine whether increased female gender representation in mathematics increases the likelihood of seeing more female-identifying mathematicians. In doing so, we hope to address the benefit of representation in mathematics and other STEM fields as student populations in these institutions grow more diverse.