No-exclaves percolation

• Published in: Journal of the Korean Physical Society Vol. 81; no. 7; pp. 680 - 687
• Main Authors: Gwak, Sang-Hwan, Goh, K.-I.
• Format: Journal Article
• Language: English
• Published: Seoul The Korean Physical Society 01.10.2022; Springer Nature B.V
• Subjects: Clusters; Collapse; Complex systems; Damage; Empirical analysis; Mathematical and Computational Physics; Nodes; Original Paper - Cross-Disciplinary Physics and Related Areas of Science and Technology; Particle and Nuclear Physics; Percolation; Perturbation; Phase transitions; Physics; Physics and Astronomy; Theoretical; Transition points; Two dimensional analysis; Percolation theory; Network robustness; Complex network; No-exclaves percolation
• ISSN: 0374-4884; 1976-8524
• DOI: 10.1007/s40042-022-00549-0

Network robustness has been a pivotal issue in the study of system failure in network science since its inception. To shed light on this subject, we introduce and study a new percolation process based on a new cluster called an ‘exclave’ cluster. The entities comprising exclave clusters in a network are the sets of connected unfailed nodes that are completely surrounded by the failed (i.e., nonfunctional) nodes. The exclave clusters are thus detached from other unfailed parts of the network, thereby becoming effectively nonfunctional. This process defines a new class of clusters of nonfunctional nodes. We call it the no-exclave percolation cluster (NExP cluster), formed by the connected union of failed clusters and the exclave clusters they enclose. Here we showcase the effect of NExP cluster, suggesting a wide and disruptive collapse in two empirical infrastructure networks. We also study on two-dimensional Euclidean lattice to analyze the phase transition behavior using finite-size scaling. The NExP model considering the collective failure clusters uncovers new aspects of network collapse as a percolation process, such as quantitative change of transition point and qualitative change of transition type. Our study discloses hidden indirect damage added to the damage directly from attacks, and thus suggests a new useful way for finding nonfunctioning areas in complex systems under external perturbations as well as internal partial closures.