Resilience Phase Transitions in Networks with Heterogeneous Node Growth Rules
Year: 2026
Type: article
Abstract: Network growth and node-removal robustness are often compared while node arrivals and link budgets also vary. We hold these two quantities fixed using the email-Eu-core and CollegeMsg temporal communication networks and vary only the selection of older attachment targets. Uniform, degree-only, activity-only, combined degree-activity, and hybrid kernels are evaluated with 30 independent graph realizations per setting. Random failures use 50 deletion orders per graph; intentional attacks use static degree, exact static betweenness, and degree recalculated after every deletion. Uncertainty is summarized by realization-level 95% confidence intervals. Under static degree attack, the mean integrated robustness falls from 0.456 to 0.313 for email-Eu-core and from 0.388 to 0.176 for CollegeMsg when uniform attachment is replaced by the combined kernel. Both single-factor kernels are less damaging than their combination, and the ranking of the five counterfactual rules is unchanged under adaptive degree removal. The combined kernel has higher intact-network global efficiency but lower random-failure robustness than uniform attachment in both data sets; no universal reversal between random and intentional attacks is observed. Susceptibility peaks are finite-network, grid-dependent fragmentation indicators, not estimates of thermodynamic critical points. The results identify how retrospective target-selection counterfactuals redistribute structural vulnerability and separate this effect from dynamical recovery.
Source: Entropy
DOI: 10.3390/e28101135
Authors: Wanjing He, Yufeng Zhuang, Yanzhu Hu
Institution: Beijing University of Posts and Telecommunications
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7222046306
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