Finding network communities using modularity density

Federico Botta, Charo del Genio

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
41 Downloads (Pure)


Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.
Original languageEnglish
Article number123402
JournalJournal of Statistical Mechanics: Theory and Experiment
Publication statusPublished - 19 Dec 2016
Externally publishedYes

Bibliographical note

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.


  • Complex Networks
  • Community Detection
  • Network Algorithms
  • Modularity Density


Dive into the research topics of 'Finding network communities using modularity density'. Together they form a unique fingerprint.

Cite this