2007/10/31 by Gunjan Agarwal, Gaurav Agarwal, David Kempe · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algorithm #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #Computer science #Graph #Graph partition #Graph theory and applications #Linear programming #Mathematical optimization #Mathematics #Maximization #Modularity (biology) #Partition (number theory) #Rounding #Theoretical computer science #physics.data-an
paper · pdf · doi:10.1140/epjb/e2008-00425-1
Submitted to EPJB. 9 pages, 3 EPS figures
arxiv created 2008/04/19 · openalex publication_date 2008/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In many networks, it is of great interest to identify "communities", unusually densely knit groups of individuals. Such communities often shed light on the function of the networks or underlying properties of the individuals. Recently, Newman suggested "modularity" as a natural measure of the quality of a network partitioning into communities. Since then, various algorithms have been proposed for (approximately) maximizing the modularity of the partitioning determined. In this paper, we introduce the technique of rounding mathematical programs to the problem of modularity maximization, presenting two novel algorithms. More specifically, the algorithms round solutions to linear and vector programs. Importantly, the linear programing algorithm comes with an a posteriori approximation guarantee: by comparing the solution quality to the fractional solution of the linear program, a bound on the available "room for improvement" can be obtained. The vector programming algorithm provides a similar bound for the best partition into two communities. We evaluate both algorithms using experiments on several standard test cases for network partitioning algorithms, and find that they perform comparably or better than past algorithms.