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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. (C) 2015 Elsevier B.V. All rights reserved.
In the past decade, sediment connectivity has become a widely recognized characteristic of a geomorphic system. However, the quantification of functional connectivity (i.e. connectivity which arises due to the actual occurrence of sediment transport processes) and its variation over space and time is still a challenge. In this context, this study assesses the effects of expected future phenomena in the context of climate change (i.e. glacier retreat, permafrost degradation or meteorological extreme events) on sediment transport dynamics in a glacierised Alpine basin. The study area is the Sulden river basin (drainage area 130 km(2)) in the Italian Alps, which is composed of two geomorphologically diverse sub-basins. Based on graph theory, we evaluated the spatio-temporal variations in functional connectivity in these two sub-basins. The graph-object, obtained by manually mapping sediment transport processes between landforms, was adapted to 6 different hydro-meteorological scenarios, which derive from combining base, heatwave and rainstorm conditions with snowmelt and glacier-melt periods. For each scenario and each sub-basin, the sediment transport network and related catchment characteristics were analysed. To compare the effects of the scenarios on functional connectivity, we introduced a connectivity degree, calculated based on the area of the landforms involved in sediment cascades. Results indicate that the area of the basin connected to its outlet in terms of sediment transport might feature a six-fold increase in case of rainstorm conditions compared to "average " meteorological conditions assumed for the base scenario. Furthermore, markedly different effects of climate change on sediment connectivity are expected between the two sub-catchments due to their contrasting morphological and lithological characteristics, in terms of relative importance of rainfall triggered colluvial processes vs temperature-driven proglacial fluvial dynamics.