Structural Vulnerability in Hierarchical Networks: A Dependency-, Redundancy-, and Level-Aware Framework and Its Empirical Limits

Abstract

Classical node-importance measures (degree, betweenness, closeness, eigenvector, PageRank, k-core) are defined solely as functions of the adjacency structure of a graph and, by construction, contain no term for hierarchical level, dependency direction, or the horizontal-versus-vertical origin of redundancy. Building on a targeted synthesis of the graph-theoretic, network-science, and hierarchy-quantification literatures, this study shows that this representational gap is real but narrower than informally claimed in prior discussions: it manifests specifically in the regime where hierarchical stratification co-occurs with horizontal (same-level) redundancy, rather than in hierarchy alone. A directed, stratified network is formalized with an explicit weighted dependency correspondence and a threshold survival rule, from which a family of node-level vulnerability scores is derived, built from a downstream dependency footprint, a dependency-concentration term, a redundancy margin, and a topology-only fallback. The framework is validated computationally on 96 synthetic network instances (perfect trees, degree-matched Erdős–Rényi and Barabási–Albert nulls, and tree-plus-horizontal-edge hybrids; 7,440 node-level observations). Results are reported symmetrically rather than selectively: the proposed score substantially outperforms classical centrality on hierarchical-plus-redundant topologies for predicting dependency-propagated cascade damage, but is outperformed by classical centrality when the damage target is purely topological efficiency loss, and performs worse than random removal when used as a sequential attack-ranking heuristic. The framework is presented as a scoped, conditionally validated contribution, with explicit statements of which claims rest on synthetic simulation only and which prior hypotheses were deliberately excluded for lack of primary-source verification.