# Correlation-Based Community Detection

## TL;DR

This paper introduces correlation-based evaluation functions for community detection that address the resolution limit problem and improve detection accuracy, supported by a new algorithm called CBCD.

## Contribution

The paper presents a novel correlation analysis framework for community detection, unifying existing functions and proposing the CBCD algorithm that outperforms current methods.

## Key findings

- CBCD outperforms existing algorithms on benchmark networks.
- Correlation functions mitigate the resolution limit problem.
- The framework unifies and improves community evaluation metrics.

## Abstract

Mining community structures from the complex network is an important problem across a variety of fields. Many existing community detection methods detect communities through optimizing a community evaluation function. However, most of these functions even have high values on random graphs and may fail to detect small communities in the large-scale network (the so-called resolution limit problem). In this paper, we introduce two novel node-centric community evaluation functions by connecting correlation analysis with community detection. We will further show that the correlation analysis can provide a novel theoretical framework which unifies some existing evaluation functions in the context of a correlation-based optimization problem. In this framework, we can mitigate the resolution limit problem and eliminate the influence of random fluctuations by selecting the right correlation function. Furthermore, we introduce three key properties used in mining association rule into the context of community detection to help us choose the appropriate correlation function. Based on our introduced correlation functions, we propose a community detection algorithm called CBCD. Our proposed algorithm outperforms existing state-of-the-art algorithms on both synthetic benchmark networks and real-world networks.