Network geography: relations, interactions, scaling and spatial processes in GIS

This chapter argues that the representational basis of GIS largely avoidseven the most rudimentary distortions of Euclidean space as reflected, forexample, in the notion of the network. Processes acting on networks whichinvolve both short and longer term dynamics are often absent from GIscience. However a sea change is taking place in the way we view thegeography of natural and man-made systems. This is emphasising theirdynamics and the way they evolve from the bottom up, with networks anessential constituent of this decentralized paradigm. Here we will sketchthese developments, showing how ideas about graphs in terms of the waythey evolve as connected, self-organised structures reflected in theirscaling, are generating new and important views of geographical space.We argue that GI science must respond to such developments and needs tofind new forms of representation which enable both theory andapplications through software to be extended to embrace this new scienceof networks

Metric and topo-geometric properties of urban street networks: some convergences, divergences, and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Metric and topo-geometric properties of urban street networks: some convergences, divergences and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Economic Geography and the Evolution of Networks

An evolutionary perspective on economic geography requires a dynamic understanding of change in networks. This paper explores theories of network evolution for their use in geography and develops the conceptual framework of geographical network trajectories. It specifically assesses how tie selection constitutes the evolutionary process of retention and variation in network structure and how geography affects these mechanisms. Finally, a typology of regional network formations is used to discuss opportunities for innovation in and across regions.evolution, network trajectory, evolutionary economic geography, social network analysis, innovation

Applications of Evolutionary Economic Geography

This paper is written as the first chapter of an edited volume on evolutionary economics and economic geography (Frenken, K., editor, Applied Evolutionary Economics and Economic Geography, Cheltenham: Edward Elgar, expected publication date February 2007). The paper reviews empirical applications of evolutionary economics in the field of economic geography. The review is divided in four parts: the micro-level of the firm, the meso-levels of industry and network, and the macro-level of spatial system. Some remarks on evolutionary policy in regional development are added as well as a short discussion of empirical problems that remain.

Decoding the urban grid: or why cities are neither trees nor perfect grids

In a previous paper (Figueiredo and Amorim, 2005), we introduced the continuity lines, a compressed description that encapsulates topological and geometrical properties of urban grids. In this paper, we applied this technique to a large database of maps that included cities of 22 countries. We explore how this representation encodes into networks universal features of urban grids and, at the same time, retrieves differences that reflect classes of cities. Then, we propose an emergent taxonomy for urban grids

Multiple centrality assessment in Parma : a network analysis of paths and open spaces

One of the largest of Europe, the recently realized university campus 'Area of the Sciences' in Parma, northern Italy, has been planned for a comprehensive programme of renovation and revitalization with a special focus on vehicular accessibility and the quality of open spaces. As part of the problem setting phase, the authors, with Rivi Engineering, applied Multiple Centrality Assessment (MCA) - a process of network analysis based on primal graphs, a set of different centrality indices and the metric computation of distances - in order to understand why the existent system of open spaces and pedestrian paths is so scarcely experienced by students as well as faculty and staff members and why it appears so poorly supportive of social life and human exchange. In the problem-solving phase MCA was also applied, turning out to offer a relevant contribution to the comparative evaluation of two alternative proposed scenarios, leading to the identification of one final solution of urban design. In the present paper, the first professional application of MCA, an innovative approach to the network analysis of geographic complex systems, is presented and its relevance in the context of a problem of urban design illustrated

Two betweenness centrality measures based on Randomized Shortest Paths

This paper introduces two new closely related betweenness centrality measures based on the Randomized Shortest Paths (RSP) framework, which fill a gap between traditional network centrality measures based on shortest paths and more recent methods considering random walks or current flows. The framework defines Boltzmann probability distributions over paths of the network which focus on the shortest paths, but also take into account longer paths depending on an inverse temperature parameter. RSP's have previously proven to be useful in defining distance measures on networks. In this work we study their utility in quantifying the importance of the nodes of a network. The proposed RSP betweenness centralities combine, in an optimal way, the ideas of using the shortest and purely random paths for analysing the roles of network nodes, avoiding issues involving these two paradigms. We present the derivations of these measures and how they can be computed in an efficient way. In addition, we show with real world examples the potential of the RSP betweenness centralities in identifying interesting nodes of a network that more traditional methods might fail to notice.Comment: Minor updates; published in Scientific Report