2013/02/23 by Tanmoy Chakraborty, Sriram Srinivasan, Chakraborty, Tanmoy +7
Computer Science · Mathematics · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Graph theory and applications #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #cs.SI #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1302.5794
31 pages, 9 figures
arxiv created 2013/02/23 · openalex publication_date 2013/02/23 · arxiv updated 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Identifying community structure is a fundamental problem in network analysis. Most community detection algorithms are based on optimizing a combinatorial parameter, for example modularity. This optimization is generally NP-hard, thus merely changing the vertex order can alter their assignments to the community. However, there has been very less study on how vertex ordering influences the results of the community detection algorithms. Here we identify and study the properties of invariant groups of vertices (constant communities) whose assignment to communities are, quite remarkably, not affected by vertex ordering. The percentage of constant communities can vary across different applications and based on empirical results we propose metrics to evaluate these communities. Using constant communities as a pre-processing step, one can significantly reduce the variation of the results. Finally, we present a case study on phoneme network and illustrate that constant communities, quite strikingly, form the core functional units of the larger communities.