Use of graph theory to study connectivity and regionalisation of the Polish urban network

Abstract

This paper uses graph theory to analyse the cohesion and regionalisation of an urban settlement network. The vertices show cities (as points), while the edges reflect distances between the cities located no farther than 25 km apart. As a research area, towns were selected that had the administrative status of cities in Poland in 2002. After an investigation of the graph theory literature, the properties of simple graphs were used to analyse the network, including full, regular, connected, and biconnected graphs. The question posed was: how coherent is a connected graph? Namely, how many edges have to be removed from a graph for it to become disconnected? For this reason, “weak points” were sought in the graphs: null graphs, bridges, and articulation points. It was assumed that the network of cities represented by a graph creates a regular and biconnected network in areas where it is permanently formed. This provided the basis for identifying areas with distinctly urbanised settlement networks. The indexes proposed by Kanski, which can be used for comparative studies, were also used to evaluate coherence. Owing to the functions provided by GIS tools and, in particular, the utilisation of additional layers with rivers, communication routes, and the historical borders of Poland over the last millennium, the interpretation of graph connectivity was able to take historical features into account. The shapes of the graphs and their degrees of connectivity described the properties of the regional settlement networks in Poland, while the historical interpretation allowed us to discuss the historical conditions leading to the formation of these networks. The analysis was conducted using GIS tools.

Visual Analysis to Assess Attraction and Organisation of Contemporary Metropolitan Systems—A Case Study of Central and Northern Italy

“…Graph theory is a branch of mathematics developed by the Swiss physicist Euler in the 18th century [49] that enables the identification and description of system elements and the description and computation of the relationships between them [54]. The discipline, as mentioned above, has found application in various research areas such as in the study of economic and social systems [55][56][57]; the study of infrastructure and transportation [58,59]; applications in urban and spatial planning [60][61][62]; and the analysis of ecological systems [63,64]. In particular, graph theory has demonstrated its adaptability for analysing commuter flows [65][66][67].…”