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

## TL;DR

This paper studies how bacterial protein interaction networks withstand node failures, revealing how network resilience relates to centrality measures and evolutionary design.

## Contribution

The study introduces a Node Resilience (NR) index to quantify network resilience and reveals its distinct correlation patterns with centrality measures.

## Key findings

- Bacterial PPI networks show biphasic resilience degradation with accelerated collapse beyond a critical threshold.
- Node Resilience (NR) strongly correlates negatively with Betweenness Centrality (BC), unlike other centrality measures.
- Evolutionary modular design buffers local failures but fails under inter-modular bridge depletion.

## Abstract

Protein-protein interaction (PPI) networks serve as the central framework for deciphering the modular structure of cellular functions and signal transduction mechanisms. While established network topological Measures (such as degree centrality, betweenness centrality, and closeness centrality) can statically characterize nodal connectivity density or pathway intermediation capacity, they fail to dynamically capture cascade following node failure.

This study employs systems biology approaches to quantitatively analyze network resilience based on bacterial PPI network data obtained from the Stanford Network Analysis Platform (SNAP). First, a progressive node removal strategy was implemented to simulate cascading failure propagation and evaluate system-level resilience degradation dynamics. Subsequently, single-node knockout experiments were systematically conducted to quantify local topological disruption effects, with network fragmentation metrics (e.g., giant component size decay rate) being integrated to establish the Node Resilience (NR) index. To validate the biological relevance of NR, we developed a multidimensional analytical framework that performs cross-correlation analysis between NR and classical centrality measures [Degree centrality (DC), Betweenness centrality (BC), Closeness centrality (CC), Eigenvector centrality (EC)], enabling systematic revelation of consensus vital nodes identified by both approaches, and unique sensitive nodes detectable only through resilience-oriented perturbation analysis.

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.