Defining and identifying communities in networks

TL;DR

This paper introduces two quantitative definitions of communities in networks, integrates them into existing algorithms, and proposes a new local algorithm that is faster and effective for large-scale networks, demonstrated on real-world data.

Contribution

It provides a formal, quantitative framework for defining communities and develops a new efficient local algorithm for community detection in large networks.

Findings

New definitions enable fully self-contained algorithms.

The proposed local algorithm outperforms existing methods in speed.

Effective detection of communities in large real-world networks.

Abstract

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic, cellular or protein networks) or technological problems (optimization of large infrastructures). Several types of algorithm exist for revealing the community structure in networks, but a general and quantitative definition of community is still lacking, leading to an intrinsic difficulty in the interpretation of the results of the algorithms without any additional non-topological information. In this paper we face this problem by introducing two quantitative definitions of community and by showing how they are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a new local algorithm to detect communities which outperforms the existing algorithms with respect to the computational cost, keeping the same level of reliability. The new algorithm is tested on artificial and real-world graphs. In particular we show the application of the new algorithm to a network of scientific collaborations, which, for its size, can not be attacked with the usual methods. This new class of local algorithms could open the way to applications to large-scale technological and biological applications.