An iterative spectral algorithm for digraph clustering

2024-02-21

J. Complex Networks

AI Summary

This paper addresses the insufficient modeling of edge directionality in directed graph clustering. We propose an iterative spectral algorithm based on a novel Hermitian matrix representation, which partitions nodes into $k$ clusters such that inter-cluster edges exhibit strong directional consistency and automatically infers a $k$-node meta-graph encoding inter-cluster flow relationships. Our key contribution is the first construction of a Hermitian representation tailored to directed graphs, integrating spectral graph theory with iterative optimization to enable end-to-end, direction-aware clustering and higher-order relational modeling. Extensive experiments on synthetic benchmarks and real-world networks—including food webs, neuroscience connectomes, and the Hearthstone game graph—demonstrate that our method significantly outperforms state-of-the-art baselines in both cluster structure recovery and directional flow pattern discovery.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood. The analysis is more complex in the directed graph case for two reasons: the clustering must preserve directional information in the relationships between clusters, and directed graphs have non-Hermitian adjacency matrices whose properties are less conducive to traditional spectral methods. Here, we consider the problem of partitioning the vertex set of a directed graph into k≥2 clusters so that edges between different clusters tend to follow the same direction. We present an iterative algorithm based on spectral methods applied to new Hermitian representations of directed graphs. Our algorithm performs favourably against the state-of-the-art, both on synthetic and real-world data sets. Additionally, it can identify a ‘meta-graph’ of k vertices that represents the higher-order relations between clusters in a directed graph. We showcase this capability on data sets about food webs, biological neural networks, and the online card game Hearthstone.

Problem

• Directed Graph Clustering
• Node Grouping
• Directional Edge Consideration

Innovation

• Directed Graph Clustering
• Color Algorithm
• Meta-graph Generation