Topological approach to analyzing compactness and connectivity of settlement systems considering terrain constraints (case study of the Saratov Region)

The article examines the application of topological concepts for analysing the structure and assessing the compactness of a regional settlement system. A methodology is proposed that adapts classical topological invariants to evaluate real transport-planning networks using OpenStreetMap data, taking into account physical-geographical and legislative constraints. Instead of abstract node connectivity indices in the settlement system graph, a new operational indicator – the “exit index” – is introduced. This index represents the number of physical, nondead-endroad exits from asettlement and is used to identifystructural vulnerabilities by analysing “articulation points” (i.e.,critical nodeswhose removal would disconnect the network). The proposed methodology was tested on the case of Saratov Oblast to assess settlement compactness and calculate new optimal connections within the settlement system, incorporating existing data on terrain, specially protected natural areas, and zones with special conditions for land use.