SPANGEO Multi-level modelling of Spatial Networks in Geography

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1 1 Action de Recherche en Amont MASSE DE DONNÉES SPANGEO Multi-level modelling of Spatial Networks in Geography scientific description of the project 1. Goal and context In their study of transportation and communication systems, economic and social networks or urban systems, geographers are more and more often confronted with matrices of increasing size, and hence increasingly difficult to analyze and represent. The complexity of these networks, at various space scales, makes the simultaneous representation of the constituting sub-graphs difficult; grasping the totality of the network and identifying its multilevel nature represents a real challenge to the geographer, who might fail to achieve a complete and proper understanding of the system by lack of adapted analytical and representational tools. Taking into account the recent methods based on the concept of small worlds or scaling networks (underlying among other things the emergence and spatial diffusion of the innovations) is definitely relevant in the operational approach of the geographical networks (Uzzi, Spiro, 2004; Fleming, 2004). Existing softwares helping to model and represent these graphs (like UCINET [USA, Social network analysis Software] or PAJEK [Slovenia, Program for Broad Network analysis]), have moreover been the subject of significant developments (Graph Drawing Conferences). However, those tools are not, in their current state, very adapted to the geographical problems and to the cartographic conventions. Also, more specialized existing software remains heavily dependent upon particular environments and hence difficult to open to methodological developments and transfers of data. The present project aims at designing and developing operational methods of modelling and representing multilevel space networks in a way adapted for geographical purposes. A first collaboration between UMR ESPACE, LIRMM and University of Montreal (on multilevel representation of the air passenger traffic worldwide network) has produced a very significant contribution in the modelling and the visualization of spatial networks (Amiel and al., 2005). However, many aspects have to be carefully re-examined and developed before proposing the existing methodological tool to the community of researchers in geography. The method for constructing multilevel graphs must be adapted and looked at in deeper details for various geographical problems (valuated, weighted or directed graphs, hypergraphs). The construction

2 2 SPANGEO by Amiel et al. partly involved a statistic computed from the network topology and related to the theory of small world networks. This first attempt must be confronted with various centrality measures that constitute alternative possible candidates for the construction of a multilevel representation of the network. The method by Amiel & al. was implemented with the software TULIP (Bordeaux 1) and involved several additions to the existing libraries. A future version must also integrate methodologies developed by systemic geography (construction of specialized indices of dependence or vulnerability). Moreover, graphical conventions have been for a long time developed in cartography. It is mandatory to see how those conventions can be integrated in the software because of their strong semantic implications (proportional size of the nodes, of the edges, distances between nodes, colours of nodes and colours of edges). The intended cooperation between geographers and computer scientists aims at producing methods, algorithms and tools able to deal with large geographical matrices and to implement a set of approaches for modelling and representing these graphs. Developing methods and software tools offering a multilevel treatment of the graphs dedicated to the fields of geography and related disciplines makes a collective and inter-disciplinary effort necessary: it is expected that the experience and expertise of the various working groups (in particular INRETS [Lille], UMR CITERES [Tours], University of Montreal, University of Lausanne and UMR ESPACE) will mutually complete and stimulate each other. The diffusion of these methods and tools in the geographical scientific community will allow a better operational approach of spatial networks and a better definition of social and territorial consequences of their evolutions. 2. Project description Multilevel networks emerge from geographical problems under different denominations and subthemes: space segregation, mobility space, exchanges of goods, services, information, economic networks or power networks. The multilevel approach of these geographical networks offers promising prospects for a better comprehension of the associated social phenomena since the problems change their nature according to the scales but space can be used as interface between them (Mathis, 2003, p.358). 2.1 Graphs in Geography and in Social Sciences For years, the search for operational and adapted solutions in problems involving networks has attempted to import available results in the theoretical literature on graphs (Nuysten & Dacey, 1961; Bank, 1970; Magnanti & Wong, 1984; Bissor & Alamdari, 1998; Guimera & Al, 2005). Work applied on social networks has demonstrated the effectiveness and productivity of small worlds networks on the production and on the diffusion of the innovations (Uzzi, Spiro, 2004). These results have a major interest for the studies on the local and regional development (Flemming, 2004). However, it is still necessary to define further the relevant regional scales, the measures of their delimitations and the nature of the charts likely to give an account of the latter in a convincing way.

3 SPANGEO Modelling and representing multi-level spatial networks The project aims at designing and developing operational methods of modelling and representation of multilevel spatial networks for the geographical issues. A first collaboration between UMR ESPACE, LIRMM and University of Montreal, on the multilevel representation of the air passenger traffic worldwide network, has produced very interesting contributions in the modelling and the visualization of the space networks (fig.1). These levels of networks reveal the most connected groups of cities to the world network (major hubs) (fig.2), as well as the subsystems that are organized more marginally (like the Asian network, or the secondary European cities).

4 4 SPANGEO This method has to be further developed, in particular in geography where the question of the multiple levels of scales and cohesion is essential, but where convenient specific models and associated tools are yet lacking to a large extent. Typically and in particular, the mode of delimitation of areas or proximities constitutes a central characteristic of the geographical field. A sound description and analysis of clusters of nodes would constitute a contribution that can reveal itself as crucial in many fields of the geographical approaches of the networks (a). In each approach, the partitioning of the network into strongly connected sub-graphs has a meaning, which must however be adapted to the types of graphs under consideration (b). In addition, cartographic conventions must be integrated into the representations of these multilevel networks (c). 2.2.a Geographical data matrices The elementary networks of the geography, like roads, railroad etc. can be represented by graphs. The introduction of traffics, exchanges and interactions modifies the apprehension of these networks and calls for a valued graphs approach. In addition, the importance of the nodes (airport cities, hubs, or multimode platform of goods) obliges to work on weighted graphs. If one further takes into account the asymmetry of the exchanges, in particular on topics relating to the

5 SPANGEO 5 migrations, dissymmetric exchanges or decision-making powers (like the corporate networks), the graphs have to be directed in addition. Also, hypergraphs are required if multiple relations are to be considered. The geographical approach thus makes it possible to consider and explore different types of graphs to study various aspects of same phenomena. We have thus tried to gather a large variety of situations involving spatial networks, in order to enrich and stimulate the development of common tools. Therefore, various types of large matrices will be analyzed: - transport systems: world network of passengers air traffic [Amiel]; European motorway and road networks, railroads valued by exchanges, access times [Chapelon] or even more or less synchronized schedules [L Hostis]; - transnational firms networks linking World and European cities: investigations carried out on three dates (1990; 1996; 2005 [Rozenblat]) will allow to approach dynamic world metropolises in the globalisation of the companies; - daily migrations from a commune to another, around centers of employment (file MIRABEL, INSEE, IFS, Switzerland), or displacements for access to services (French communal Inventory) make it possible to delimit basins of life; at another scale, the interregional migration data inside and between the European countries will serve to define strongly cohesive and interacting transnational areas (Weidlich, Haag, 1998); - systems of territorial actors exchanging information or sharing common interests [Larribe; Cadoret]: these networks can be valuated (even negatively in the event of conflicts), balanced according to the importance of the territories or actors brought into play, or differentiated by their types. This information will be the subject of a comparative collection as well as standardization of the data. In each field, the geographers will establish the state of the existing sources and the methods and software to analyze and to represent them. These sources will be confronted with the assistance of data processing specialists in order to select the data that seem most relevant and promising with the questions under concern. All these geographical graphs will constitute various examples permitting to approach and treat different questions and problems. Each data set will exhibit specificities in its nature, and also form the involved levels of spatial organization. However, all sets share the common point to be modelled as graphs with places identified as nodes and exchanges as links; they integrate the same approach to spatial networks, aimed at identifying coherent systems of organization. 2.2.b Partitioning according to local cohesions These networks admit levels of spatial organization that vary not only from one indicator to another, but also for the same indicator from one territory to another. For example, the north American air network is fairly more integrated than its European counterpart. In another register, the systems of daily labour migrations have a more important and wider space bursting around the large metropolises than around a small borough, unless the latter possesses particular economic functions. A technique developed by Auber et al. (2003) proceeds by deleting some edges of a related graph in order to break up it into subgraphs. These subgraphs, correspond to the strongly connected components of the graph, highlighted by the removing of the edges contributing less to local connectivities. The procedure can be repeated on each subgraph, thus producing a hierarchy of nested subgraphs.

6 6 SPANGEO Filtering edges A filtering is carried out on the basis of the value associated with each edge, the latter being a measure of its contribution to the local connectivity of its neighbours. The index of cohesion of an edge is to some extent a generalization of the index of clustering introduced by Watts and Strogatz into their small worlds network analysis (Watts, Strogatz, 1998; Watts, 1999). This index of cohesion is obtained by calculating the ratio between the number of effective links between the neighbours of the incidental nodes to the edge and the maximum number of links that could be observed. Among the neighbours of the two incidental tops to the edge, it is necessary to distinguish their common neighbours (the Wuv unit on the figure) and those, which are close only to the one of the two nodes (fig.3). Wuv Mu = Nu \ Nv Mv = Nv \ Nu u v Nu : Mu Wuv The distribution of the edges cohesion index (fig.4) permits to fix a threshold under which edges are removed. This threshold can be determined according to a quality indicator ( MQ(t) ) borrowed from Mancoridis (1998), to some extent similar to other criteria proposed through the literature (Alpert, Kahng, 1995; Berkhin, 2002).

7 SPANGEO 7 However, the method of Auber et al. (2003) relies entirely upon the topology of the studied network, watching on its small worlds properties, without taking into account other important properties of the graphs like the magnitude of the exchanges, the physical or temporal distances, the orientation of the graphs or their qualitative differences. To obtain a relevant delimitation of the sub-networks it is necessary to adapt the methodology of Auber et al. (2003) and its current interface (TULIP) according to these various properties. - Weighted Graphs: the weight of the edges of the graph, if it follows a scale-free distribution, accounts for the strong hierarchy of inter-connected network. In order to take these weights into account, we suggest to examine the values obtained by multiplying the index of cohesion of the edges by their respective weights. The valuated graphs can also be partitioned by the criterion of the minimum normalized cut, which consist in partitioning the graph in two complementary parts so that the sum of flows between the two parts (divided by the totality of internal and external flows associated the smallest part) reaches its minimal value H (Cheeger s constant). Reiterating the process yields a downward hierarchical classification of the nodes of the graph. Another alternative is the spectral clustering (Alpert et al ) consisting in ordering the nodes according to the values they take on the first eigenvector of the Laplacian of the valued graph (Chung 1997) and then assigning the nodes of positive sign to a class, and nodes of negative sign to the complementary class. Various variants will be tested and compared in order to define the indices and optimality criteria most adapted to the geographical problems. - Directed Graphs: the asymmetry of the exchanges, distances, domination relations etc. requires a particular emphasis on the directed graphs, often used in geography to conceptualize center-periphery oppositions. The integration of this orientation of the graphs in initial methodology will be based on the work already undertaken in this field (Bavaud F, 2002). - Hypergraphs: as a possible option of analysis, interactions of multiple types will be considered and integrated within the hypergraphs paradigm, involving distinct types of edges (Bank, 1987; Finke, 2001). Measures and indices Various existing and new measures of cohesion, equivalence, similarities, scale invariance etc will be considered and applied for characterizing the graph and sub-graphs properties; those indices will be integrated in the final representation of the partitioned graphs. 2.2.c Cartography Semantic The representation of the graphs and their partitions is a considerable stage in their restitution, their analysis and their interpretation. Graphic conventions have for a long time been developed in cartography. They carry information and meaning (size of the nodes, of the edges, distances between the nodes, colors of the nodes and of the edges, etc) to be incorporated into the graphic interfaces (Pumain, Beguin, 1994; L Hostis, 2003). Choices will be carried out in agreement with the specialists in cartography in order to significantly enrich the representative ability

8 8 SPANGEO of the graphic interface. Thus validated options of forms of representation will be developed which will guide the non-specialist user: - the nodes surface could be made proportional to the weight of the nodes which it gathers (as measured by the totality of the exchanges, the accessibility in the network or an external criterion), that is to say with their cohesion ; - the nodes colour could indicate different types of nodes or relative indicators (ratio) which one can calculate (accessibility compared to the weight; various densities). Screens of gradations colours adapted to the types of discounted qualifiers will be proposed to the users; - the edges length will be determined by the magnetism of proximity in the graph; - the edges thickness could be proportionally defined with various indicators of weight of the exchanges; - the edges colour could be differentiated according to types of links (for the hypergraphs), or according to the local density of the edges. The report/ratio of the representations between the various levels will be the subject of a very detailed attention. Indeed, two successively encased levels will have to show links of relationship (form or colour) while being differentiated according to their own respective level (size or intensity of colour). The distances between the levels (qualified by different levels of cohesion) will be visualized by the reports/ratios of size of the groups of nodes. In animated representation (already permitted by TULIP software), the access times towards the coherent groups have to be higher than the access times towards the less coherent groups. The current development of research in animated cartography could be fed by this type of application (L Hostis, 2003). 2.3 Approach developed upstream by software specialists and geographers The close cooperation between geographers and data processing specialists then aims at producing a tool able to treat large geographical matrices, and to offer a variety of modelling and representation methods, either tested and validated or in exploratory phase. The diffusion of this tool in the geographical environments will allow a better operational approach towards spatial networks, in particular the social and territorial consequences of their evolutions. This collaboration with the interface between Geography and Data processing is intended for a reciprocal enrichment of the two disciplines: new problems involving broad and complex data for the data processing specialists; new operational tools bringing original and meaningful perspectives for the geographers. Moreover, the cooperation and sharing of tools between geographers working on differing matrices involving distinct spatial and time scales will offer the opportunity to produce a progress report on the contributions of the visions small worlds and scale-invariant networks for understanding interdependence and exchange phenomena in the geographical space.

9 SPANGEO 9 3. Intended results The development of the data-processing tool of treatment and its diffusion are envisaged over three years. This work will involve the participation of software specialists, of cartographers, of geographers specialized in spatial analysis, but also of geographers working on various themes involving large and various spatial exchange matrices. A survey will be installed to continuously monitor the current and undergone work, its relevance to the developed problems (regarding the most recent publications) as well as its updating with respect to the data availability and the developed solution. A workshop will be organized every 6 months in order to give an account of it (members of the group and specialized guests). Two CDD positions (one in software development and the other in geography) will be required all the way long in order to build the data-processing tools while integrating the two disciplines in order to facilitate their diffusion in the scientific circles. In particular, the CDD geographer will at the beginning be in charge of the geographical databases documentation so that the data processing specialists can exploit them. This work of documentation and working of the data bases will have to be completed by the geographers involved in the project, who will ensure the structuring of the data ontology (Smith and Mark 2001), their collection, their setting (data bases) and their exploitation (extractions): hence, data processing specialists are guaranteed to have access to documented material and to benefit from geographical expertise. Integration and a formalization of the geographical knowledge will be carried out in the data bases by first documenting and consolidating the bases, then by extracting the relevant data (for example, for the time data: extraction of time arcs, time ways, ways as given by the Web site Amadeus, minimal ways rebuilt with the MapNod model, etc.). The articulation and the visibility of the modules will have to be coherent both for the geographers and for the sofware specialists. Their development and their access will be carried out collectively. A methodological user s guide will be elaborated and made accessible, in view of a broader diffusion, to the non-specialized scientific user. First year - collection and standardization of data; - confrontation of geographical and data-processing models; - software developments which will validate this confrontation; - definition of the modules to be developed and the general graphic interface; - installation of the data-processing and geographical survey; - publications (papers in international reviews, European and world conferences). Second year - installation of modules and general graphic interface; - development of the software and validation of the modules; - data-processing and geographical survey; - publications (papers in international reviews, European and world conferences). Third year - installation of a site of access to the software accompanied by a methodological guide of use; - diffusion of the tools and methodologies by a multidisciplinary school CNRS; - data-processing and geographical survey; - publications (papers in international reviews, European and world conferences).

10 10 SPANGEO 4. References Alpert, C.J. and A.B. Kahng (1995). Recent Developments in Netlist Partitioning: A Survey. Integration: the VLSI Journal, 19(1-2): p Alpert C.J., Kahng A.B., Yao S. (1999). «Spectral partitioning : The more eigenvectors, the better» Discrete Applied Math Vol.90, pp Amaral, L. A. N., Scala, A., Barthelémy, M. & Stanley, H. E. (2000). Classes of small-world networks. Proc. Nat. Acad. Sci. USA 97, Amiel, M., Mélançon G., Rozenblat C. (2005). Réseaux multi-niveaux : l exemple des échanges aériens mondiaux, M@ppemonde, n 3 (à paraître) Auber, D. et al. (2003). Multiscale Navigation of Small World Networks. In IEEE Symposium on Information Visualisation, Seattle, GA, USA. IEEE Computer Science Press. Bavaud F. (2002). «The Quasisymmetric Side of Gravity modelling» Environment and Planning A Vol.34, pp Berge Cl. (1970). Graphes, Dunod, Paris. Berge Cl. (1987). Hyper Graphes, Bordas, Paris. Bisseur A., Alamdari F. (1998) Factors affecting the operational success of strategic airline alliances. Transportation 25, (1998). Berkhin, P. (2002). Survey of Clustering Data Mining Techniques. Accrue Software: San Jose, CA. Burghouwt, G., Hakfoort, J., Ritsema van Eck, J., (2003). The spatial configuration of airline networks in Europe. Journal of Air Transport Management 9, p Chiricota, Y., Jourdan F., Melançon G. (2002). Clustering as a Strategy for the Visualization of Large Graphs : A Metric-Based Approach. In DIMACS Workshop on Data Mining and Visualization, DIMACS Center, Rutgers University. Chung F. (1997). «Spectral Graph Theory» CBMS Regional Conferences Series 92, American Mathematical Society Guimera R., Mossa S., Tutschi A., Amaral A.N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities global roles. Proc Natl Acad Sci USA.;102(22): Finke G. (2001). Recherche opérationnelle et réseaux. Hermès, Paris Fleming L., Charles King III, Juba A. (2004). Small worlds and regional innovative advantage, Working paper, Harvard University. L Hostis A., «De l Espace contracté à l espace chiffonné, apports de l animation à cartographie en relief d espace-temps». - Revue Internationale de Géomatique, n 13, p animations sur fr Magnanti T.L., R. T. Wong, (1984). Network Design and Transportation Planning: Models and Algorithms. Transportation Science 18, Mancoridis, S. et al. (1998). Using Automatic Clustering to Produce High-Level System Organizations of Source Code. Mathis Ph. (dir.) (2003). Graphes et réseaux: modélisation multi-niveau, Hermès Lavoisier, 361 p. NuystenJ.D., Dacey M.F. (1961) A graph theory interpretation of nodal regions, Regional Science Association, Papers and Proceedings, 7, O Connor, K. (2003). Global air Travel: toward concentration or dispersal? Journal of Transport Geography 11, p Smith B., Mark D.M. (2001). Geographical categories : an ontological investigation. International Journal of Geographical Information Science, 15 (7),

11 SPANGEO 11 Strogatz, S. H. (2001). Exploring complex networks. Nature 410, Uzzi B., Spiro J. (2004).Collaboration and creativity: The Small World problem, Working paper Weber, M., William, G. (2001). Drivers of long-haul air transport route development. Journal of Transport Geography 9, p Watts, D.J., Strogatz. S.H. (1998.). Collective Dynamics of Small-World Networks. Nature, 393: p Watts, D.J.. (1999). Small Worlds. Princeton University Press Weidlich W. Haag G. (Eds.) (1988). «Inter-regional Migration» Springer, Berlin Wijk, J.v., Ham. F.v. (2004). Interactive Visualization of Small World Graphs. In IEEE Symposium on Information Visualisation, Austin, TX, USA. IEEE Computer Science press. 5. Bibliographical references of the researchers involved in the project Céline Rozenblat Publications : Rozenblat C. (2004). Tissus de villes. Réseaux et systèmes urbains en Europe. Habilitation à diriger des recherches, Université Montpellier III., 191 p. Rozenblat C., Cicille P. (2003). Les villes européennes, analyse comparative. DATAR La Documentation française, 94 p. (translated in German by BBR). Bretagnolle A., Pumain D., Rozenblat C. (1998). «Space-time contraction and the dynamics of Urban Systems», Cybergeo, 61, 13 p., Pumain D., Rozenblat C. (1993). «The location of multinational firms in the European urban system». Urban Studies, 10, Scientific Organisation and promotion of geographical models : Rozenblat C., Chéry J-P., Tannier C. (2002). Direction of the Spatial modelling web site (GDR Libergeo) : : based on C.Rozenblat et J-P. Chéry (2001). CNRS multidisciplinary school on Spatial modelling (Montpellier). Magali Amiel Amiel, M., Melançon G., Rozenblat C. (2005). Multi-level networks: the case of world air traffics. 14th European Colloquium on Theoretical and Quantitative Geography, Tomar (Portugal). Amiel, M., Mélançon G., Rozenblat C. (2005). Réseaux multi-niveaux : l exemple des échanges aériens mondiaux, M@ppemonde, n 3 (à paraître)

12 12 SPANGEO Guy Mélançon Chiricota, Y., F. Jourdan, Melançon G. (2004). Metric-Based Network Exploration and Multiscale Scatterplot. IEEE International Symposium on Information Visualization, Austin, Texas, USA, IEEE Computer Science Press. Auber, D., Y. Chiricota, Melançon G (2003). Multiscale navigation of Small World Networks. IEEE Symposium on Information Visualisation, Seattle, GA, USA, IEEE Computer Science Press. Delest, M., B. Leblanc, et al. (2001). Graph Visualization and Navigation as an Interface to Data Exploration. Colloque Veille Stratégique, Scientifique et Technologique VSST 2001, Barcelone 15-19/10/2001. Herman, I., Marshall M. S., Melançon G.. (2000). Density Functions for Visual Attributes and Effective Partitioning in Graph Visualization. IEEE Symposium on Information Visualization (InfoVis 2000), Salt Lake City, Utah, U.S., IEEE Computer Society. Herman, I., M. S. Marshall, Melançon G. (2000). Graph Visualisation and Navigation in Information Visualisation: A Survey. IEEE Transactions on Visualization and Computer Graphics 6(1): François Boutin Boutin Fr., Thièvre J., Hascoët M.(2005). Multilevel Compound Tree: Construction Visualization and Interaction, Proceedings of Interact 2005, Lecture Notes in Computer Science, Springer. Boutin Fr., Hascoët M.(2004). Focus Dependent Multi-level Graph Clustering. Proceedings of AVI 2004, ACM, Boutin Fr., Hascoët M.(2004). Multi-Level Exploration of Citation Graphs. Proceedings of ECDL 2004, Springer, Boutin Fr., Hascoët M.(2003). Focus-Based Clustering for Multi-Scale Visualization. Proceedings of IV 2003, IEEE, pp 53-59, François Bavaud Bavaud F (1998). Models for spatial weights: a systematic look. Geographical Analysis Vol. 30, Bavaud F. (2001). The quasi-symmetric side of gravity modelling. Environment and Planning A 34/1, Bavaud F. (2003). Une approche markovienne générale à l analyse spatiale. In: Actes des XXXVèmes Journées de Statistique, Société Française de Statistique, Alain L Hostis Software : L Hostis A., Chapelon L (2000). logiciel MapNod pour la modélisation et la représentation des réseaux de transport voir Publications : L Hostis A. (2003). «De l Espace contracté à l espace chiffonné, apports de l animation à cartographie en relief d espace-temps». - Revue Internationale de Géomatique, n 13, p animations sur L Hostis A. (2003). «Théorie des graphes et représentation des distances : chronocartes et autres

13 SPANGEO 13 représentations» in Graphes et réseaux, modélisation multiniveaux, Mathis Ph. (direction), volume du traité d Information Géographique et d Aménagement du Territoire (IGAT), Série aspects fondamentaux de l analyse spatiale, Hermès Lavoisier. L Hostis A. (2000). «Multimodalité et intermodalité dans les transports» in Atlas de France, Volume Transport et Énergie, Chapelon L, Saint Julien Th. (coord), Montpellier/Paris : GIP Reclus/La Documentation Française, 2000, p L Hostis A. (1996). «Transports et Aménagement du territoire : cartographie par images de synthèse d une métrique réseau». - Mappemonde, n 3. - p Laurent Chapelon Chapelon L. (1997). Offre de transport et aménagement du territoire: evaluation spatio-temporelle des projets de modification de l offre par modélisation multi-échelles des systèmes de transport, Thèse de doctorat, Université de Tours. Chapelon L. (1998). Evaluation des projets autoroutiers: vers une plus grande complémentarité des indicateurs d accessibilité. Les Cahiers Scientifiques du transport, 33, Appert M., Chapelon L. (2002). Planification des transports régionaux en Languedoc-Roussillon et Nord Pas de Calais: evaluation de la concurrence rail-route. Programme de recherché INRETS/GRRT UMR ESPACE, Montpellier Chapelon L., Saint-Julien Th. (Dir.) (2000). Atlas de France Transport et énergie. Paris, Reclus-La Documentation Française. Sébastien Larribe Larribe S. (2003). Des réseaux sociaux au sociographe pour l analyse des jeux d acteurs, in: MATHIS Ph. (dir.). Graphes et Réseaux, modélisation multiniveau Paris: Lavoisier, Hermès 358 p. Larribe S. (1999). Représentations auto-centrées et interactives d un réseau d acteurs en aménagement, Thèse de doctorat, Tours.