Background: Human cancers are driven by interacting genetic, epigenetic, transcriptomic and microenvironmental programs. Pan-cancer resources such as The Cancer Genome Atlas (TCGA) have shown that tumors originating from different organs share recurrent oncogenic pathways, while organ-specific cancers retain distinctive transcriptional, stromal, immune and metabolic contexts. Weighted co-expression networks are useful for prioritizing cancer genes, but conventional thresholding may remove weak yet structurally essential cross-module edges. Objective: This study extends the h-cutoff method from weighted network analysis to cancer transcriptomics. The method uses co-expression or co-occurrence values as continuous edge weights, applies a one-order h-cutoff to define an h-subnet, restores high-betweenness weak bridges to form an h-backbone, and then applies a two-order h-cutoff within the h-backbone to identify final Core genes. The present version explicitly positions the study as a methodological framework and compact computational demonstration rather than a completed raw-matrix empirical reanalysis. Methods: A macro-combined to micro-separated design was adopted. The pan-cancer layer models a shared proliferative and survival backbone across multiple solid tumors, while organ-specific layers focus on glioblastoma (GBM), liver hepatocellular carcinoma (LIHC), lung adenocarcinoma (LUAD) and kidney renal clear cell carcinoma (KIRC). The preferred data sources are TCGA Pan-Cancer Atlas, TCGA-GBM, TCGA-LIHC, TCGA-LUAD, TCGA-KIRC and external Gene Expression Omnibus (GEO) validation cohorts. The mathematical framework was formalized for non-integer biological weights through continuous h-strength, rank-space interpolation, weak-bridge recovery and node-level two-order h-cutoff. The compact dataset is used to demonstrate the workflow and figure generation; publication-grade empirical analysis should recompute all edge weights from raw or uniformly processed matrices. Results: In the compact demonstration network, the pan-cancer h-backbone prioritized BIRC5, CDK1, TPX2, MKI67, AURKA, TOP2A, CCNB1 and PCNA, consistent with a shared mitotic and proliferative core. The GBM-specific layer emphasized TYROBP, SYP, ANXA5, CD44 and EGFR; the LIHC layer emphasized AURKA, BUB1B, CCNA2, PRC1, TOP2A and PTTG1; the LUAD layer emphasized SPP1, IL6, CDH1, PECAM1, EPCAM and KRT19; and the KIRC layer emphasized VHL, HIF1A, CA9, VEGFA, ALDH2, ACADM and PTPRC. These results illustrate how h-cutoff separates a pan-cancer proliferative backbone from organ-specific immune, epithelial, neuronal, hepatic and metabolic modules. These outputs are interpreted as demonstration results, not as definitive raw-database-derived empirical findings. Conclusions: Continuous h-cutoff offers an adaptive and interpretable framework for extracting cancer gene backbones from dense weighted networks. It complements standard WGCNA and pathway analysis by preserving both strong functional edges and weak structural bridges. The accompanying data package provides compact network tables, figures and scripts for re-running the pipeline on full TCGA/GEO expression matrices. The framework is ready for a subsequent full empirical biomedical data-analysis paper in which all compact edge weights are replaced by raw-matrix-derived networks.
Ying Ye (Wed,) studied this question.