Alzheimer’s disease (AD) and Parkinson’s disease (PD) are polygenic neurodegenerative disorders in which disease genes act through immune, glial, proteostatic, metabolic, synaptic, and vascular networks rather than through isolated single-gene effects. This methodological framework introduces continuous h-cutoff as an adaptive strategy for reducing dense weighted biological networks while preserving weak but structurally important bridges. Co-expression or co-occurrence values are normalized into continuous edge weights. A first-order h-cutoff defines the functional h-subnet, after which high-betweenness weak bridges are restored to construct the h-backbone. A second-order h-cutoff is then applied within the backbone to prioritize candidate hub genes. The framework is illustrated with a compact, evidence-derived demonstration dataset organized into AD/PD-shared, AD-specific, and PD-specific layers, using public resources including GSE48350, GSE26927, GSE174367, GSE161045, and the National Institute on Aging Genetics of Alzheimer’s Disease Data Storage Site. The demonstration highlights shared neurodegenerative modules involving CXCR4, FLT1, HSPB1, HSPA1A, CALM3, CDC42, RAB3A, TREM2, and APOE, as well as AD-specific glial-lipid and mitochondrial candidates and PD-specific proteostasis, synaptic, and dopaminergic candidates. These outputs are intended as a reproducible computational proposal rather than a completed raw-matrix reanalysis. Full empirical validation will require uniformly processed expression or pseudobulk matrices to recompute edge weights and to assess robustness through sensitivity analyses, functional enrichment analyses, and replication in independent cohorts. This study explicitly highlights two key innovations: (i) continuous h-strength interpolation, which enables fractional biological edge weights, and (ii) a two-stage hierarchical cutoff strategy that first constructs an h-backbone network and subsequently identifies hub genes within that backbone.