Defining and identifying communities in networks

TLDR

Community detection is a key problem across social, biological, and technological domains, yet existing algorithms lack a general quantitative definition, making result interpretation difficult. The authors aim to illustrate how quantitative community definitions can be incorporated into existing algorithms and to introduce a local algorithm that matches reliability while reducing computational cost. They test the local algorithm on artificial and real‑world graphs, including a large scientific collaboration network that is infeasible for conventional methods. The resulting algorithms become fully self‑contained, successfully identify communities in large networks, and suggest applicability to large‑scale technological and biological systems.

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 and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community 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 local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.