The Popularity-Homophily Index: A new way to measure Homophily in Directed Graphs

Abstract: In networks, the well-documented tendency for people with similar characteristics to form connections is known as the principle of homophily. Being able to quantify homophily into a number has a significant real-world impact, ranging from government fund-allocation to finetuning the parameters in a sociological model. This paper introduces the Popularity-Homophily Index (PH Index) as a new metric to measure homophily in directed graphs. The PH Index takes into account the popularity of each actor in the interaction network, with popularity precalculated with an importance algorithm like Google PageRank. The PH Index improves upon other existing measures by weighting a homophilic edge leading to an important actor over a homophilic edge leading to a less important actor. The PH Index can be calculated not only for a single node in a directed graph but also for the entire graph. This paper calculates the PH Index of two sample graphs and concludes with an overview of the strengths and weaknesses of the PH Index, and its potential applications in the real world.