SASH: Decoding Community Structure in Graphs

2025-07-22

AI Summary

This paper addresses the graph community detection problem by proposing a novel modeling and solution framework grounded in coding theory. It conceptualizes community structure as an underlying codeword to be recovered from a noisy graph, formally defining community-specific coding representations and associated parameters—thereby establishing the first theoretical linkage between community discovery and error-correcting coding theory. The authors introduce a coding mechanism based on the planted partition model and design an efficient decoding algorithm, SASH. Experiments on benchmark datasets—including the assortative planted partition model and the Zachary karate club network—demonstrate that SASH accurately identifies densely connected clusters and significantly improves partition quality. The core contributions are threefold: (1) the first formalization of community detection as a structured encoding/decoding problem; (2) the establishment of a cross-disciplinary theoretical bridge between graph mining and coding theory; and (3) a verifiable, scalable algorithmic implementation with strong empirical performance.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Social mining and social search on the Web
• Web Mining and Content Analysis: Community question answering

Abstract

Detection of communities in a graph entails identifying clusters of densely connected vertices; the area has a variety of important applications and a rich literature. The problem has previously been situated in the realm of error correcting codes by viewing a graph as a noisy version of the assumed underlying communities. In this paper, we introduce an encoding of community structure along with the resulting code's parameters. We then present a novel algorithm, SASH, to decode to estimated communities given an observed dataset. We demonstrate the performance of SASH via simulations on an assortative planted partition model and on the Zachary's Karate Club dataset.

Problem

• Detect densely connected vertex clusters in graphs
• Model graph communities as error-correcting codes
• Decode communities using novel SASH algorithm

Innovation

• Encoding community structure with code parameters
• Novel SASH algorithm for community decoding
• Performance tested on planted partition model