Graph theory—Recent developments of its application in geomorphology

• Although geomorphic systems have been depicted as networks, graph theory has seldom been applied.
• Graph theory makes system structure quantifiable and comparable.
• We show examples dealing with networks representing spatial and nonspatial geomorphic systems.
• Perspectives for graph theory applications include scale linkage, historical contingency, connectivity, sediment transfer, and natural hazards.

Applications of graph theory have proliferated across the academic spectrum in recent years. Whereas geosciences and landscape ecology have made rich use of graph theory, its use seems limited in physical geography, and particularly in geomorphology. Common applications of graph theory—analyses of connectivity, path or transport efficiencies, subnetworks, network structure, system behaviour and dynamics, and network optimization or engineering—all have uses or potential uses in geomorphology and closely related fields. In this paper, we give a short introduction to graph theory and review previous geomorphological applications or works in related fields that have been particularly influential. Network-like geomorphic systems can be classified into nonspatial or spatially implicit system components linked by statistical/causal relationships and spatial units linked by some spatial relationship, for example by fluxes of matter and/or energy. We argue that, if geomorphic system properties and behaviour (e.g., complexity, sensitivity, synchronisability, historical contingency, connectivity etc.) depend on system structure and if graph theory is able to quantitatively describe the configuration of system components, then graph theory should provide us with tools that help in quantifying system properties and in inferring system behaviour.