Resilience and evolutionary insights in PPI networks: comparative analysis of node resilience and centrality measures

Our systematic node removal simulations revealed biphasic resilience degradation across bacterial PPI networks: progressive node failure induced gradual resilience decay whereas exceeding a critical threshold for each network triggered accelerated collapse. This phase transition aligns with evolutionary design principles - modular architectures buffer localized perturbations through functional redundancy, but inter-modular bridge depletion beyond criticality propagates cascading failures via weakly coupled connections. Notably, NR exhibited a strong negative correlation with BC, contrasting with weak associations for DC, CC, and EC. This dichotomy arises because BC quantifies cross-modular information brokerage - high-BC nodes act as structural keystones whose removal disconnects functional modules, drastically reducing global entropy. Conversely, for DC, CC, and EC primarily reflect local connectivity patterns with limited cascade propagation potential.