Galois's algebraic structure and bipartite graph spatio-structural analytics for urban public transportation system assessment

The analysis of complex systems remains the domain of excellence to grasp for control complexity. Theoretical foundations derived from order theory (Galois lattice, spectral analysis of discrete graphs) provide interesting solutions to study exchanges and flows in a system. These are systemic tools well suited to big linked data mining. Various applications exist in the areas of computer networks, social networks analysis, economic analysis and, knowledge discovery. This paper involves Galois Lattice operations and centrality based on spectral analysis for the discovery of the organization and the existing linkage between transport supply given by the routes served by transport (bus, tram, train) and demand resulting in spatial zones (the stop stations). The main objective of this work is to develop a structural knowledge and patterns discovery framework to discover deep knowledge ensuing from the structural representation of the public transport network. The case study concerns the analysis of urban transportation systems (tram and bus) of the city of Valenciennes (France). However, the approach remains valid for other networks without any alterations or modifications.