Diverted, non-dendritic flow is widespread in hydrologic networks and influences flood forecasting, water-quality assessments, and aquatic habitat analysis, yet this type of flow is inadequately supported by traditional dendritic data structures and algorithms. The hydrofabrics (defined as holistic systems of data that represent the cascade of catchments, waterbodies, flow connectivity, and linked points of interest) that do represent non-dendritic flow have developed independent encodings without shared formalization. This study addresses this gap by making three contributions toward a common foundation. First, it presents a small collection of graph and database patterns – self-referencing, junction, and catchments-as-edges tables, plus primary-path designation – that span the structural choices observed across hydrofabrics internationally. Second, it develops reusable algorithms for non-dendritic networks: network navigation with primary-path filtering, divergence-aware stream order, and a bridge-based total-accumulation procedure. The accumulation procedure uses Tarjan's bridge-finding algorithm to partition the network into a dendritic backbone and diversion groups, then runs bounded local searches within each group. This gives effectively linear scaling on networks dominated by dendritic structure, where the brute-force alternative is quadratic. Formal correctness and complexity arguments are provided, and the procedure complements prior spectral graph-theoretic methods developed for delta channel networks by targeting total drainage accumulation at hydrofabric scale. Third, it applies the patterns and algorithms across six hydrofabrics – NHDPlusV2, NHDPlusHR, the Australian Geofabric, Canada's National Hydro Network, the pan-European EU-Hydro, and the global GRIT (Global RIver Topology) – to give the first, to the authors' knowledge, cross-fabric measurement of non-dendritic prevalence. The measurements show that diverted flow is a pervasive feature of digital hydrography globally. These patterns and algorithms are realized in implementations such as a hydrography data model and a software library. Rather than proposing a comprehensive framework, the paper offers a minimum yet sufficient toolkit: a shared vocabulary for comparing, integrating, and extending non-dendritic hydrologic software across organizational and national boundaries.