Critical Correlation Threshold (r*) Reveals Reduced Network Cohesion in TCGA-BRCA Tumor Gene Expression

Cancer is fundamentally a systems-level disease characterized not only by changes in individual genes but by large-scale reorganization of molecular interaction networks. Traditional biomarker approaches focus on differential expression of single genes, yet they often fail to capture the global structural transitions that accompany tumor initiation and progression. To address this limitation, we developed the MAXINFO framework, a computational method designed to quantify systemic network instability in cancer using gene expression–derived correlation networks. MAXINFO is based on the analysis of algebraic connectivity (λ₂), a graph-theoretic measure that reflects the structural integrity and cohesion of a network. By constructing correlation networks from gene expression profiles and progressively applying increasing correlation thresholds, we identify a critical transition point, denoted r*, defined as the first threshold at which the network loses global connectivity. This transition represents a phase-like structural breakdown of coordinated gene regulation. We applied MAXINFO to The Cancer Genome Atlas (TCGA) breast cancer (BRCA) cohort, comparing tumor and normal tissue samples. Our results reveal a clear and reproducible shift in the critical connectivity threshold between normal and tumor networks. Specifically, tumor networks exhibit network fragmentation at lower correlation thresholds than normal tissue, indicating reduced structural robustness and increased systemic instability. This finding is consistent with the biological expectation that cancer disrupts coordinated regulatory programs and introduces widespread regulatory noise. Importantly, the r* metric captures a global network property that cannot be reduced to individual gene effects. Instead, it reflects an emergent characteristic of the system as a whole. This systems-level biomarker has the potential to complement traditional differential expression analysis by providing a quantitative measure of network-scale deregulation. Beyond breast cancer, the MAXINFO framework is designed to be generalizable across cancer types and other biological conditions. Because it operates directly on gene expression data without requiring prior pathway annotation, it enables unbiased detection of structural transitions in molecular networks. The broader significance of this work lies in its potential applications for cancer research and clinical translation. The r* metric may serve as a novel biomarker for: • quantifying tumor-specific network instability• comparing different cancer types• tracking disease progression• evaluating treatment response• identifying early systemic changes preceding phenotypic transformation Furthermore, MAXINFO provides a foundation for exploring cancer as a network phase transition, offering a new conceptual and quantitative framework for understanding oncogenesis. Future research directions include extending the method to additional TCGA cohorts, integrating multi-omics data, investigating prognostic associations with patient outcomes, and exploring whether r* can predict therapeutic sensitivity or resistance. By focusing on emergent structural properties rather than individual molecular components, MAXINFO represents a shift toward a systems-level understanding of cancer and provides a novel computational tool for network-based cancer research.