The concept of polycentric social and economic systems is a vital representation of a highly effective system. From the neoclassical economics point of view, the competition between economically equal-powered centres leads to better and faster development of regional economic systems. The Netherlands is a chrestomathic and a classical example of such a system with it’s widely known urban agglomeration called Randstad as a four-piece urban agglomeration.

However, the structure of Randstad is not floating in a vacuum. It’s surrounded by vast suburbs and other cities important for regional parity. Also, Randstad is being reshaped with urban growth processes as the spatial patterns of daily trips change. This processes differentiate the polycentricity in two different aspects. The first is named the morphological polycentricity. This term stands for relative homogeneity of internal characteristics of nodes in polycentric system (for this study — the municipalities as the socio-geographical units, involved in interactions with the others). The other aspect is functional polycentricity, which refers to the homogeneity of interactional patterns. Both interactions and importance of a system in a whole geographical system can be quantified via commuting of people.

In this study, we examine spatial and temporal changes in the polycentric structure of the Netherlands as a whole throughout 2004—2017 period. The data is a set of mobility surveys results — Mobiliteitsonderzoek Nederland (MON), Onderzoek Verplaatsingen in Nederland (OViN) — which are held in the Netherlands annually. These datasets provide us the information about short-term travelling in the country, such as workers commuting, shop trips etc. Reshaping this data into a set of correspondence matrices and then to graph representation with the nodes as Netherlands municipalities and edges as interaction intensiveness between each pair, we defined morphological and functional network characteristics as follows.

The morphological characteristic of a node in a system is random walk betweenness centrality measure, as it reflects both topological characteristics and weights taking into account a degree of transit through the node. So, the morphological polycentricity is the homogeneity of centrality measures.

As for the measurement of functional polycentricity, we’ve decided to use functional regionalisation of networks through percolation regions modelling. This way of modelling the regions shows hierarchical regions structure in networks. Proposed by H. Rozenfeld and D. Rybski and further developed by E. Arcaute and M. Batty, this method was used primary without deploying to a conceptual framework of non-network nature.

It has a significant advantage in performance and spatial interpretability of results compared to conventional algorithms. We’ve implemented this modelling using DBSCAN clustering with different noize filters. Using this, we’ve differentiated the hierarchical regions’ cores by their sustainability, or the number of clustering iterations before they are included into the top-level cluster. The functional polycentricity is the regions cores sustainability homogeneity in this case.

Results of polycentricity evaluation in morphological aspect are somewhat predictable. The four main municipalities of the Randstad (Amsterdam, Hague, Rotterdam and Utrecht) are stable in the top-tier of municipalities centrality measures through all the yearly timeframes 2004—2017. Although the distribution itself is stable in both spatial and temporal ways, there are still changes in order of municipalities in the rank-size distribution. Except for the tail for the distribution, the lower the rank in this distribution the more changes of municipalities in each rank. The mentioned tail, however, is low in changes — these are the municipalities of Frisian Islands. Moreover, the centrality is highly correlated with socio-economic measures of place prosperity (functional diversity, for instance), so these conclusions can be correspondent to regional statistics.

From a functional perspective, however, the Netherlands is not a polycentric country. In terms of hierarchical regions core sustainability, it has one dominant centre — Amsterdam, and this disparity between the Amsterdam-related region and the rest of the country grows. All the municipalities included in the Randstad agglomeration are highly connected to each other and as the strength of the interaction grows, it becomes almost impossible to delineate the separate cores in this de-facto united city. However, some of the peripheral centres have relatively high sustainability because of geographical distance to the Randstad. These are Groningen, Leeuwarden, Maastricht, Tilburg.

The strength of connections between municipalities volatiles greatly but with no significant spatial pattern. This refers us to the idea of a complex system itself, as it’s self-regulatory ability reshapes and balances the weights of connections. It’s the reaction to multiple socio-economic changes in the Netherlands such as the rapid growth of population and functional diversity in Flevoland province.

Methodologically, random walk betweenness centrality showed satisfactory results in the quantification of morphological characteristics. The regions modelling through percolation and DBSCAN still needs validation on a territory with completely different inhabitation patterns, different population density and longer distances between municipalities in extremum.