Abstract
AbstractConnecting nodes that contingently co-appear, which is a common process of networking in social and biological systems, normally leads to modular structure characterized by the absence of definite boundaries. This study seeks to find and evaluate methods to detect such modules, which will be called ‘pervasive’ communities. We propose a mathematical formulation to decompose a random walk spreading over the entire network into localized random walks as a proxy for pervasive communities. We applied this formulation to biological and social as well as synthetic networks to demonstrate that it can properly detect communities as pervasively structured objects. We further addressed a question that is fundamental but has been little discussed so far: What is the hierarchical organization of pervasive communities and how can it be extracted? Here we show that hierarchical organization of pervasive communities is unveiled from finer to coarser layers through discrete phase transitions that intermittently occur as the value for a resolution-controlling parameter is quasi-statically increased. To our knowledge, this is the first elucidation of how the pervasiveness and hierarchy, both hallmarks of community structure of real-world networks, are unified.
Funder
Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Reference75 articles.
1. Fortunato, S. & Hric, D. Community detection in networks: A user guide. Phys. Rep. 659, 1–44 (2016).
2. Peel, L., Larremore, D. B. & Clauset, A. The ground truth about metadata and community detection in networks. Sci. Adv. 3, e1602548 (2017).
3. Palla, G., Derenyi, I. & Vicsek, T. Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005).
4. Airoldi, E. M., Blei, D. M., Fienberg, S. E. & Xing, E. P. Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9, 1981–2014 (2008).
5. Lancichinetti, A., Fortunato, S. & Kertesz, J. Detecting the overlapping and hierarchical community structure in complex networks. New J. Phys. 11, 033015 (2008).