Resilience Phase Transitions in Networks with Heterogeneous Node Growth Rules

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.

Authors

Institutions

Publication Details

Journal
Entropy
Published
2026-10-15
DOI
https://doi.org/10.3390/e28101135
Primary Topic
Complex Network Analysis Techniques
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Resilience Phase Transitions in Networks with Heterogeneous Node Growth Rules

Yanzhu Hu, Yufeng Zhuang, Wanjing He
Entropy
Complex Network Analysis Techniques
article

Resilience Phase Transitions in Networks with Heterogeneous Node Growth Rules

Yanzhu Hu, Yufeng Zhuang, Wanjing He
article en

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.

EntropyVol. 28(10)
Beijing University of Posts and Telecommunications (CN)
Openalex Percentile: Top 13%
Complex Network Analysis Techniques
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.