Extending the Walktrap Algorithm to Directed Graphs via Hitting Time and Stationary Distribution

Meeting ID: 891 3406 2450

Passcode: 123456

Abstract: Community detection has been extensively studied through a wide range of algorithms. One of the most influential methods for undirected graphs is the Walktrap algorithm, which estimates distances between vertices via random walks and evaluates communities based on modularity derived from vertex degrees. While several attempts have been made to adapt this method to directed graphs, they have achieved limited success.

In this talk, I will revisit the Walktrap algorithm (Pons and Latapy, J. Graph Algorithms Appl., 10:191–218, 2006) and present an extension that is suitable for directed graphs. The key idea is to redefine the distance between vertices using the hitting time and the stationary distribution of a random walk. These definitions are both theoretically grounded and computationally efficient, as they rely on well-established algorithms. Notably, this framework also recovers the undirected case as a special instance. Finally, I will present an implementation of the proposed algorithm and discuss its practicality and effectiveness through experiments.

This work is based on joint research with Phan Thị Hà Dương and Đặng Tiến Đạt.