2013/10/30 by Angsheng Li, Li, Angsheng, Jiankou Li +3
Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Social Media and Politics #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.1310.8294
openalex publication_date 2013/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Community detecting is one of the main approaches to understanding networks \citeFor2010. However it has been a longstanding challenge to give a definition for community structures of networks. Here we found that community structures are definable in networks, and are universal in real world. We proposed the notions of entropy- and conductance-community structure ratios. It was shown that the definitions of the modularity proposed in \citeNG2004, and our entropy- and conductance-community structures are equivalent in defining community structures of networks, that randomness in the ER model \citeER1960 and preferential attachment in the PA \citeBar1999 model are not mechanisms of community structures of networks, and that the existence of community structures is a universal phenomenon in real networks. Our results demonstrate that community structure is a universal phenomenon in the real world that is definable, solving the challenge of definition of community structures in networks. This progress provides a foundation for a structural theory of networks.