Globalisation and interregional exchange of people, goods, and services has boosted the importance of and reliance on all kinds of transport networks. The linear structure of road networks is especially sensitive to natural hazards. In southern Norway, steep topography and extreme weather events promote frequent traffic disruption caused by debris flows. Topographic susceptibility and trigger frequency maps serve as input into a hazard appraisal at the scale of first-order catchments to quantify the impact of debris flows on the road network in terms of a failure likelihood of each link connecting two network vertices, e.g. road junctions. We compute total additional traffic loads as a function of traffic volume and excess distance, i.e. the extra length of an alternative path connecting two previously disrupted network vertices using a shortest-path algorithm. Our risk metric of link failure is the total additional annual traffic load, expressed as vehicle kilometres, because of debris-flow-related road closures. We present two scenarios demonstrating the impact of debris flows on the road network and quantify the associated path-failure likelihood between major cities in southern Norway. The scenarios indicate that major routes crossing the central and north-western part of the study area are associated with high link-failure risk. Yet options for detours on major routes are manifold and incur only little additional costs provided that drivers are sufficiently well informed about road closures. Our risk estimates may be of importance to road network managers and transport companies relying on speedy delivery of services and goods.