Function-Specific Redundancy in Residential Room-Relation Graphs: A Test of Leaf-Venation-Inspired Connectivity

Reticulate leaf venation illustrates how network loops can preserve connectivity following local link loss, but their functional analog in residential room-relation graphs remains insufficiently characterized. We examined whether global cyclicity coincides with protection of specific room functions and how that protection depends on functional placement and graph assumptions. Of 3493 CubiGraph5K plan records, 863 met eligibility criteria, including 483 cyclic graphs. We quantified Entry-to-destination edge- and internally vertex-disjoint paths, compared room functions, tested degree-conditioned bedroom-label allocation, and evaluated alternative route restrictions and edge representations. Among cyclic graphs, 370/483 (76.6%) contained no bedroom with two edge-disjoint paths from the annotated Entry. Edge-protected shares were 15.8% for bedrooms (136/861), 72.6% for living rooms (368/507), and 68.5% for kitchens (332/485). The degree-conditioned benchmark predicted 155.7 protected bedrooms, compared with 270.5 under unrestricted label allocation and 136 observed. Bedroom protection was 14.4% (124/861) under internally vertex-disjoint paths, whereas excluding open-adjacency links (code 1) and retaining door-associated links (code 2) reduced edge protection from 15.8% (136/861) to 3.8% (33/861). A purpose-selected 22-plan audit flagged geometric annotation ambiguities in 11 cases. These findings provide a destination- and disruption-specific assessment of a leaf-venation-inspired connectivity principle in annotated graphs, while physical traversability and circulation resilience remain unverified.