Graph theory-based framework for Diagnosing River fragmentation and connectivity

River fragmentation and climate-driven thermal change increasingly threaten freshwater biodiversity, yet basin-scale assessments typically treat connectivity as a purely structural property, measuring whether physical pathways exist between network nodes, without considering whether organisms can realistically traverse thermally unsuitable or barrier-impeded reaches. We developed a graph-theoretic indicator suite that integrates thermal habitat classification, barrier passability, and distance-decay dispersal to quantify functional connectivity, locate confluences of elevated biophysical heterogeneity, delineate thermal refugia, and prioritise barriers for restoration under climate-warming scenarios. Applied to the Upper Colorado River Basin (132,487 nodes; 274 dams; 77,444 natural slope barriers), the framework revealed a pronounced structural–functional divergence. Although the network appeared almost fully connected in structural terms, functional connectivity represented only a minute fraction of its theoretical potential once cumulative passability losses and distance-decay dispersal were incorporated. Coldwater habitat (≤20 °C) encompassed 97% of nodes yet was fragmented into isolated high-elevation patches; two refugia above 2700 m contained approximately 60% of all coldwater nodes. Confluences ranking highest on a composite of network centrality, thermal mixing potential, and confluence degree concentrated within high-elevation coldwater reaches in the central and eastern basin. The composite selects warm-margin confluences at above-chance frequency relative to the basin-wide coldwater fraction, identifying candidate locations for biological survey rather than verified biodiversity hotspots. Because the analysis includes only inventoried dams and natural slope barriers and omits the far more numerous small structures such as culverts, road crossings, and low-head weirs, these estimates are conservative, and the true functional fragmentation of the basin is likely more severe than reported. Uniform warming increments, applied as sensitivity scenarios, indicated a 7.8-percentage-point loss of coldwater habitat under +3 °C warming, concentrated in the mid-elevation corridor connecting high-elevation refugia to downstream reaches, where three chokepoint barriers retained the highest priority under thermal perturbation, although simulated connectivity gain was not monotonic in rank. The spatial convergence of functional isolation, thermal stress, and climate vulnerability emerged only under the integrated framework, indicating that structural connectivity metrics alone do not track ecological accessibility in thermally heterogeneous river networks.