Zastosowanie metody minimalnego drzewa rozpinającego (najkrótszego dendrytu) w ocenie efektywności i spójności sieci osadniczej województwa mazowieckiego = Application of the minimum spanning tree method in assessing the effectiveness and cohesion of the settlement network of Mazowieckie voivodeship

Abstract

Contemporary settlement systems observed in Poland bear numerous traces of historical transformations of rural settlements which took place in the 19th century, at the time of foreign partitioning of Polish territory, in different ways in particular regions. The result of processes occurring from the second half of the 20th century is the extensive development of urban areas, and – after 1990 – chaotic, spontaneous processes of transformation in suburban zones. Research methods using graph theory have been applied for years in investigating settlement networks on various scales. One of the more useful graphs is the minimum spanning tree (MST), which connects all vertices in such a way that the sum of the distances between them is the shortest. This article presents the application of the minimum spanning tree (or shortest dendrite) method with a view to its suitability for determining the degree of dispersion and spatial cohesion of urbanised structures being assessed. Two indicators have been proposed thanks to alignment of the shortest dendrite length to other variables. The settlement network effectiveness indicator is the ratio of MST length to the population in an area. The settlement network cohesion indicator is in turn the ratio of the MST length to population density. Mazowieckie voivodeship has been chosen as the research area, while address points obtained from the central official database collecting data from municipal records have been chosen as the source dataset. Over 1 million address points were considered, in line with their status as at the end of 2016. Minimum spanning trees were plotted for each of the 314 gminas (local-authority areas) aking up the voivodeship, using ArcGIS software. Subsequently, the proposed indicators were calculated by reference to the MSTs. The results were then mapped. The proposed indicators may be helpful in studies on the origin of settlements, allowing areas with varying degrees of uniformity or isolation of building locations to be indicated. They can be made use of in comparative studies, especially concerning rural settlements, in which single-family housing predominates, and hamlets and uildings standing in isolation are present. The effectiveness indicator can be used in the assessment of infrastructural coverage, i.a. in the ontext of the costs of spatial chaos and demographic capacity.