Effets spatiaux et effets réseau dans l’évaluation d’indicateurs sur les nœuds d’un réseau d’infrastructure

The quantitative study of an infrastructure network in geography often consists in assessing indicators on the network components (nodes and sections). In that respect, the network is modelled by a graph whose vertices and edges respectively correspond to the nodal and linear network infrastructures. Then, such a graph can be studied thanks to tools provided by the graph theory and mainly based on the shortest paths features.The most typical indicators are accessibility (closeness from a given vertex to the others graph vertices, computed in summarizing the shortest path lengths) and centrality or “betweenness” (contribution of a given vertex or edge to the origin-destination paths, computed in counting the shortest paths passing through this component). For this reason, accessibility and centrality features of a vertex depend on the shortest paths distribution on the network, and also on the relative location of the vertex inside the network.However, the spatial location of vertices predisposes them to be accessible and central, regardless of the relational potentialities provided by the network structure. Actually, a vertex located at the centre (resp. on the periphery) of the network area is more (resp. less) likely to be accessible and central.Therefore, it seems relevant to highlight how the network makes the vertices accessible and central, independently on the advantages only provided by their spatial location. Then, we show that it is possible to make allowances for the corresponding “network and spatial effects” by comparing the shortest paths traditionnally taken into account to compute these indicators with a set of optimal paths called “Delaunay paths”.Besides the study of accessibility and centrality indicators, our method can be extended to the study of any indicator (structural or not), as long as such an indicator is usually computed from shortest paths. It finally provides a useful tool to interpret indicators on a network and to understand the networks contribution to the phenomena described by these indicators.