COMMUTERS GRAPHS AND CITIES POLYCENTRIC COHESION

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1 COMMUTERS GRAPHS AND CITIES POLYCENTRIC COHESION Céline ROZENBLAT and Patrice TISSANDIER Institute of Geography, University of Lausanne Abstract The actually urban dynamics lead to some difficulties in the global apprehension of the city. According to commuters weighted graphs between localities, we propose a new approach to understand those dynamics. Working successively on three scales (urban areas perimeters, sub-centres and each locality), the topic of this research is to measure and visualize the cohesion and the fragmentation of urban spaces. We show an empirical approach of French urban system from data of last four censuses ( ). KEYWORDS: graph, commuters, intra-urban, cohesion, fragmentation INTRODUCTION The recent urban processes show a double transformation of the cities. Firstly, at an international and national level, the concentration of economic assets increased the commandment power of the biggest cities. Secondly, at a local scale, a new distribution of population and employment is implemented, with a spread movement from the urban centre to the periphery. Thus, an increasing urban sprawl and the apparition of polycentric structures materialize the contemporary local urban dynamics. Such modifications of the traditional urban structure lead to some urban management policies difficulties. Indeed, an inadequacy appears between the urban planning, based on a halo territory, and the reticular development of the cities. The study of commuters between localities, and their representation by oriented and weighted graphs, leads to new representations perspectives, which could provide new elements for urban planning. The approach took place in the SPANGEO project (SPAtial Networks in GEOgraphy) where we are looking for new representations of cities through different types of networks ( Here, with commuters data, an example is developed from French population census for years 1975, 1982, 1990 and Three questions, which are also the three scales of the study, guide the development of this paper. Can we define urban areas at the national level by a new approach based on commuters graphs and can we compare the cohesion of such areas (1)? How can we determinate the polycentric structure of the cities and underline the cohesion v/s fragmentation of this sub-centres (2)? Can we define the role of each locality according to its position into the city polycentric structure (3)? 1- CITIES DELIMITATION AND COMPARISON OF URBAN COHESION The question of cities delimitation and their comparison in term of intra-urban organization is not already solved by the difficulty of the urban system quickly change. 1-a Urban Area Delimitation The classical method to delimitate cities, found in a lot of countries, is built on by the membership in an urban area of all localities where at least n% of active population work in the central locality or in the agglomeration area (fig.1.a). But this kind of method only takes into account the centrifuge flows and ignore others non-centrifuge flows which doesn t seems adapted to the city polycentric approach. Thus, we chose another method, based on networks commuters to incorporate into each urban area its polycentric sub-systems, which have like satellite functions (fig.1.b). Then, this method allows delimiting each city with every localities which are directly or indirectly related to the centre. Figure 1: Delimitations of the urban area a: classical delimitation b: network delimitation

2 Using a Strength clustering (see Amiel et al., 2005) we can identify, for the whole French territory, the urban area definitions (fig.2). Figure 2: Delimitation of french urban areas in b Comparison of Cohesions and Compactness of cities and Centres Centrality evaluations After having delimitated urban areas, their cohesions can be measured. Using again the small world approach, we can calculate the strength index which calculate the graph density around each edge (neighborough 3 and 4) (Chiricota et al., 2002; Auber et al. 2003; Melançon, 2006). Figure 3: Urban cohesion of Marseille and Nice in 1999 This strength index is measured for every nodes and every edges. Their average enables to compare the cohesion between two urban areas or to show the evolution of the cohesion in the same urban area. In the figure 3, the average of the strength index for Marseille (on the left) is at 0,23 (maximum of 0,78) but for Nice (on the right) only at 0,14 (maximum at 0,41). It shows a better cohesion between Marseille localities than between Nice ones.

3 For the study of the compactness of an urban area, we distinguish the number and the cohesion of sub-centres (which will be defined in point 2). With the example of Nice, still in 1999, we identify 6 subsystems, which are cities like Cannes, Antibes or Grasse and we can calculate their strength index and their closure to other centres (fig.4). Figure 4: Urban polycentrism: the case of Nice sub-centres in 1999 With the diachronic approach, we will underline the formation of those sub-systems around each cities, their rhythms and their size (fig.5). The ultimate goal is to compare at the national or international level different forming urban areas, and to make a typology of them. Figure 5: Marseille Centrality index evolution

4 The centrality index, named betweeness centrality, will complete those results, indicating the graph s most central node and especially the evolution of the central centrality of each urban area. This index is calculated by the number of shorter ways of the graph passing by each node. The betweeness centrality index of Marseille in 1999 is 1312 although the Aix en Provence one is 460 (fig.5). We can also study the evolution of this kind of indexes of the core of the cities and also compare cities according to the centrality of their core. 2- SUB-CENTERS AND ENCLOSED TERRITORIES For the identification of sub-centres, we use again strength index by using it for a clustering operation. The principle of the clustering operation is to regroup the nodes by deleting the edges with small values. In our work, this proceeding leads to the constitution of clusters regrouping localities with strong links and also show the links between the clusters. Thus, we can measure the cohesion, but also the fragmentation, between the sub-centres (fig.6). Figure 6: Clustering of Marseille Urban area in 1999 with the valuated strength index 3- LOCALITY POSITION IN THE CITY Some others indicators allow us to qualify the position of a locality in the polycentric structure of its proper urban area. For example, a node with a high degree (number of edges connected to the node) shows a core of a sub-centre, often opened with other sub-centres (fig.7). We can enlarge this approach testing all kinds of confrontations of local and global measures to find localities qualitative positions in or between sub-centers. Figure 7: The relay position of some localities according to the Guimera s relation

5 CONCLUSION Thus, with a new approach of the urban organization based on networks, and with the help of a powerful software for analyse and visualisation of the graphs (Tulip), we are able to compare the inner structures of all the French cities, from 1975 to The common processes of urban sprawl and fragmentation are developed, showing specific spaces. Those analyses provide tools to identify spatial and reticular transformations of the city, tools that can help urban planning policies to readapt and reorganize the urban coherence. REFERENCES Amiel M., Melançon G., Rozenblat C. (2005). «Réseaux muti-niveaux: l exemple des échanges aériens mondiaux». Mappemonde, Auber D., Chiricota Y., Jourdan F. and Melancon G. (2003) Multiscale visualization of small world networks. In INFOVIS '03: Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'03), pp Chiricota Y., Jourdan F. and Melancon G. (2002). Clustering as a Strategy for the Visualization of Large Graphs: A Metric-Based Approach. In DIMACS Workshop on Data Mining and Visualization. Piscataway, NJ: DIMACS Center, Rutgers University. Guimera R., Mossa S., Turtschi A., and Amaral L. A. N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities global roles, PNAS vol. 102 no. 22, pp Melançon G. (2006). Just how dense are dense graphs in the real world? A methodological note. BELIV Workshop within AVI Conference, Venice Italy. Watts D.J. (1999) Small Worlds. Princeton: Princeton University Press, 266 p. AUTHORS INFORMATION Céline ROZENBLAT celine.rozenblat@unil.ch University of Lausanne Patrice TISSANDIER patrice.tissandier@unil.ch University of Lausanne