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

TL;DR

The paper introduces the Popularity-Homophily Index (PH Index), a new metric for quantifying homophily in directed graphs by incorporating node importance, with potential applications in sociology and network analysis.

Contribution

It proposes the PH Index, which weights homophilic connections based on node popularity, improving measurement accuracy over existing methods.

Findings

PH Index accounts for node importance in homophily measurement

Applied to sample graphs demonstrating its effectiveness

Discusses strengths, weaknesses, and real-world applications

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.