No-exclaves percolation on random networks

• Published in: Chaos, solitons and fractals Vol. 184; p. 115004
• Main Authors: Min, Byungjoon, Park, Eun-Kyu, Gwak, Sang-Hwan, Goh, K.-I.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2024
• Subjects: Network robustness; No-exclaves; Percolation; Percolation; Network robustness; No-exclaves
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2024.115004

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. •We present mean-field solution to no-exclaves percolation (NExP) on random networks.•The NExP displays three phases and two transitions between them on random networks.•Two transitions in the NExP process are computed and characterized accurately.•Our results suggests an effective way to improve network robustness by the NExP rule.