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A quantitative understanding of how sediment discharge from subglacial fluvial systems varies in response to glaciohydrological conditions is essential for understanding marine systems around Greenland and Antarctica and for interpreting sedimentary records of cryosphere evolution. Here we develop a graph based approach, GraphSSeT, to model subglacial fluvial sedimentary transport using subglacial hydrology model outputs as forcing. GraphSSeT includes glacial erosion of bedrock and a dynamic sediment model with exchange between the active transport system and a basal sediment layer. Sediment transport considers transport-limited and supply-limited regimes and includes stochastically-evolving grain size, network scale flow management and tracking of detrital provenance. GraphSSeT satisfies volume balance and sediment velocity and transport capacity constraints on flow. GraphSSeT is demonstrated for synthetic scenarios that probe the impact of variations in hydrological, geological and glaciological characteristics on sediment transport over multi-diurnal to seasonal timeframes. For steady-state hydrology scenarios on seasonal timescales we find a primary control from the scale and organisation of the channelised hydrological flow network. The development of grain size dependant selective transport is identified as the major secondary control. Non-steady-state hydrology is tested on multi-diurnal timescales, for which sediment discharge scales with peak water input leading to increased sediment discharge compared to steady state. With increasing application of subglacial hydrology models, GraphSSeT extends this capacity to define quantitatively the volume, grain size distribution and detrital characteristics of sediment discharge, and enables a stronger connection of models of the glacio-hydrological system with constraints from the sediment record and impacts on marine systems. [ABSTRACT FROM AUTHOR]