Resilience of networks with community structure behaves as if under an external field

Gaogao Dong, Jingfang Fan, Louis M. Shekhtman, Saray Shai, Ruijin Du, Lixin Tian, Xiaosong Chen, H. Eugene Stanley, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic– paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

Original languageEnglish
Pages (from-to)6911-6915
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number27
StatePublished - 3 Jul 2018
Externally publishedYes


  • Community structure
  • External field
  • Percolation
  • Resilience
  • Universality

ASJC Scopus subject areas

  • General


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