Combinatorial connectivity and spectral graph analytics for urban public transportation system

Abstract Spatial structural analytics have increased importance in recent years as a helpful tool for decision making as well as public operators’ commitment in integrated transport planning and land use. Analysis of complex systems remains the domain of excellence to grasp for control complexity. The public transportation transit system assessment targets two important aspects of public transport network: the organizational diagnosis and the technical diagnosis. Theoretical foundations derived from order theory (combinatorial connectivity, spectral graphs analysis) provide interesting solutions to study exchanges and flows in a system. These are systemic tools well suited to big linked data analytics. Various applications exist in the areas of computer networks, social networks analysis, economic analysis and, knowledge discovery. This paper involves simplicial algebra and centrality based on spectral graphs for the discovery of the organization and the existing linkage between transport supply given by the routes served by transport (bus, tram, metro, train) and demand resulted in attractive spatial zones (stop stations generators). The case study concerns the analysis of urban transportation systems of the city of Valenciennes (France). However, the approach remains valid for other networks without any alterations or modifications.