Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Measurement and Analysis of Online Social Networks Systems

  • Emilio Ferrara
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_242


Community structure

Large (online) social networks are known to exhibit a community structure: nodes can be separated and grouped into (possibly overlapping) sets so that each group is densely interconnected internally and loosely connected with others


The modularity function Q has been introduced to determine the quality of the grouping structure or clustering of a given network G = (n, m) with n nodes and m edges. A network clustering is considered well founded if nodes assigned to the same cluster are tightly interconnected among each other and loosely interconnected with those assigned to other clusters. Such type of networks exhibits the so-called community structure. The modularity function is defined as follows: \( \left( Qc=\frac{1}{2m}\sum\limits_{i,j}\left[\left({A}_{i,j}-\frac{k_i\cdot {k}_j}{2m}\right)\cdot \delta \left({c}_i,{c}_j\right)\right]\right). \)

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Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Complex Networks and Systems Research, School of Informatics and ComputingIndiana UniversityBloomingtonUSA

Section editors and affiliations

  • Przemysław Kazienko
    • 1
  • Jaroslaw Jankowski
    • 2
  1. 1.Department of Computer Science and Management, Institute of InformaticsWrocław University of TechnologyWrocławPoland
  2. 2.Faculty of Computer Science and Information TechnologyWest Pomeranian University of TechnologySzczecinPoland