Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of network evolution and the emergence of structural inequalities in these network. This tutorial offers a comprehensive overview of homophily, covering its various definitions, key properties, and the limitations of widely used metrics. Extending beyond traditional pairwise interactions, we will discuss homophily in higher-order network structures such as hypergraphs and simplicial complexes. We will further discuss network generating models capable of producing different types of homophilic networks with tunable levels of homophily and highlight their relevance in real-world contexts. The tutorial concludes with a discussion of open challenges, emerging directions, and opportunities for further research in this area.

This tutorial is intended for researchers in the fields of social and complex networks who are interested in understanding network structure, advancing homophily measures, and exploring generative models. It will be particularly relevant to those studying systems where group interactions play a central role, such as social, organizational, and communication networks. Participants should have prior exposure to basic concepts in graph theory or network science. The tutorial aims to serve as a valuable resource for researchers investigating network evolution, structural inequalities, group formation, and the development of network-based models and metrics. This tutorial

1. Offers intense, short, and focused modules. 

2. Integrates homophily with algorithmic fairness. 

3. Stimulates interest and relevance of topics.

4. Opens discussion on homophily, research gaps, and future directions.

Homophily Measures in Complex Networks 

Homophilic Network Generating Models 

Dr. Akrati Saxena is an assistant professor at LIACS, the computer science and AI institute of the Faculty of Science of Leiden University, and an Adjunct Professor at the University of Victoria, Canada. Previously, she worked as a Research Fellow at Eindhoven University of Technology, Netherlands, and the National University of Singapore. She leads the AlFa (Algorithmic Fairness) research group, which develops fairness-aware heuristic, approximation, machine learning, and deep learning-based methods for complex network data. Her research interest lies at the intersection of Social Network Analysis, Complex Networks, Computational Social Science, Data Science, and Algorithmic Fairness. Her current work focuses on understanding inequalities in complex networks and advancing fairness-aware algorithms in network and data science, including analyzing biases in existing systems, defining fairness constraints and evaluation metrics, and designing fair computational frameworks. In addition to her research, she serves on the Diversity Committee at LIACS, contributing to efforts that foster inclusion and equity within the academic community. 

Gaurav Kumar is a Junior Research Fellow at Department of Physics, Indian Institute of Science Education and Research (IISER) Pune, India. He received his Master's degree in Physics from Indian Institute of Technology (IIT) Gandhinagar, India. His research interests include social network analysis, homophily and contagion models on networks.

Dr. Chandrakala Meena is an assistant professor at Indian Institute of Science Education and Research (IISER) Pune, India. She received her Ph.D. in Physics from IISER Mohali, India under supervision of Prof. Sudeshna Sinha. Her research broadly focuses on the dynamical behaviour and pattern formation in nonlinear systems and complex networks.

1. Akrati Saxena, George Fletcher, and Mykola Pechenizkiy. FairSNA: Algorithmic fairness in social network analysis. ACM Computing Surveys, 56(8):1–45, 2024. 

2. Jalali, Z.S., Introne, J. and Soundarajan, S., 2023. Social stratification in networks: insights from co-authorship networks. Journal of the Royal Society Interface, 20(198), p.20220555. 

3. Benjamin Golub and Matthew O. Jackson. How Homophily Affects the Speed of Learning and Best-Response Dynamics. The Quarterly Journal of Economics, 127(3):1287–1338, August 2012. 

4. Miller McPherson, Lynn Smith-Lovin, and James M. Cook. Birds of a Feather: Homophily in Social Networks. Annual Review of Sociology, 27(Volume 27, 2001):415–444, August 2001. 

5. Mikhail Mironov and Liudmila Prokhorenkova. Revisiting Graph Homophily Measures, December 2024. 

6. Arnab Sarker, Natalie Northrup, and Ali Jadbabaie. Higher-order homophily on simplicial complexes. Proceedings of the National Academy of Sciences, 121(12):e2315931121, March 2024. 

7. Nate Veldt, Austin R. Benson, and Jon Kleinberg. Combinatorial characterizations and impossibilities for higher-order homophily. Science Advances, 9(1):eabq3200, January 2023.