Two-way Node Popularity Model for Directed and Bipartite Networks

TL;DR

This paper introduces the Two-Way Node Popularity Model (TNPM) for directed and bipartite networks, addressing node popularity and improving community detection with novel algorithms and theoretical analysis.

Contribution

The paper proposes TNPM, a probabilistic framework that incorporates node popularity, along with the DOM and TSDC algorithms for efficient model fitting and community detection.

Findings

Enhanced estimation accuracy demonstrated in numerical studies.

Improved computational efficiency for large-scale networks.

Application to real-world data reveals insightful community structures.

Abstract

There has been extensive research on community detection in directed and bipartite networks. However, these studies often fail to consider the popularity of nodes in different communities, which is a common phenomenon in real-world networks. To address this issue, we propose a new probabilistic framework called the Two-Way Node Popularity Model (TNPM). The TNPM also accommodates edges from different distributions within a general sub-Gaussian family. We introduce the Delete-One-Method (DOM) for model fitting and community structure identification, and provide a comprehensive theoretical analysis with novel technical skills dealing with sub-Gaussian generalization. Additionally, we propose the Two-Stage Divided Cosine Algorithm (TSDC) to handle large-scale networks more efficiently. Our proposed methods offer multi-folded advantages in terms of estimation accuracy and computational efficiency, as demonstrated through extensive numerical studies. We apply our methods to two real-world applications, uncovering interesting findings.