No-exclaves percolation on random networks

Byungjoon Min, Eun Kyu Park, Sang Hwan Gwak, K. I. Goh

Research output: Contribution to journalArticlepeer-review


No-exclaves percolation (NExP) is a nonlocal percolation process in which the components are formed not only by the connected occupied nodes but also by the agglomeration of empty nodes completely surrounded by the occupied nodes. It has been studied in low dimensions, displaying such novel phenomena as the discontinuous transition to complete percolation. However, its characteristics in complex networks are still unexplored. In this paper, we study the NExP on random networks by developing mean-field solutions using the generating function formalism. Our theory allows us to determine the size of the giant no-exclaves component as well as the percolation threshold, which are in excellent agreements with Monte Carlo simulations on random networks and some real-world networks. We show that on random networks NExP exhibits three phases and two transitions between them: the phases are characterized by the presence or absence of not only the giant NExP component but also the giant unoccupied component, which is the giant connected component composed solely of unoccupied nodes. This work offers theoretical understanding on the anatomy of phase transitions in the NExP process.

Original languageEnglish
Article number115004
JournalChaos, Solitons and Fractals
Publication statusPublished - 2024 Jul

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd


  • Network robustness
  • No-exclaves
  • Percolation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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