A complex network approach to urban growth

The economic geography can be viewed as a large and growing network of interacting activities. This fundamental network structure and the large size of such systems makes complex networks an attractive model for its analysis. In this paper we propose the use of complex networks for geographical modeling and demonstrate how such an application can be combined with a cellular model to produce output that is consistent with large scale regularities such as power laws and fractality. Complex networks can provide a stringent framework for growth dynamic modeling where concepts from e.g. spatial interaction models and multiplicative growth models can be combined with the flexible representation of land and behavior found in cellular automata and agent-based models. In addition, there exists a large body of theory for the analysis of complex networks that have direct applications for urban geographic problems. The intended use of such models is twofold: i) to address the problem of how the empirically observed hierarchical structure of settlements can be explained as a stationary property of a stochastic evolutionary process rather than as equilibrium points in a dynamics, and, ii) to improve the prediction quality of applied urban modeling.evolutionary economics, complex networks, urban growth

Preferential centrality as a multi-regional model for spatial interaction and urban agglomeration

Understanding how transportation networks affect regional development has been a long-standing challenge for modellers in several disciplines, both in research and practice. Approaches span between light-weight accessibility and centrality models, to data-heavy land use-transport interaction models. Centrality models have been increasingly employed to support spatial planning on the city-scale, where such techniques are attractive due to their low requirements of socio-economic and demographic data, while they also maintain representations of essential features such as accessibility. However, it has been less clear if such approaches can be successfully extended from the urban to the regional scale. In this paper we demonstrate how a recently introduced centrality measure – preferential centrality – can be used as a modelling framework on the multi-regional scale, while retaining high intra-urban spatial resolution. Centrality is calculated on a zonal level, with local plot characteristics and network travel times as input. Preferential centrality is calculated similarly to Google PageRank and eigenvector centrality, but with preferential growth as an additional component that represents local agglomeration processes. To examine the explanatory power of this approach, we compare computed centrality with empirical land taxation values, using the southern half of Sweden as a case study area. Using a static accessibility model as benchmark, we find that the preferential model has a higher capacity to reproduce empirical patterns, with regard to geographical correlations as well as for probability distributions. Our findings suggest that preferential centrality analysis can have practical value in urban and regional planning contexts, for example when assessing the geographical distribution of impacts from transport infrastructure investments

Empirical support for a theory of spatial capital: Housing prices in Oslo and land values in Gothenburg

Land is, besides labour and capital, one of the classic production factors in economic theory. However, neoclassical economics dominating the 20thcentury, simplified production theory to only labour and capital, treating land either as just another form of capital or as the natural resources it harbours. This hides the central role of land – in the meaning of spatial extension and location – for contemporary economies, where land rent is an essential cost and location a productive factor for most economic activities, not least since these increasingly are located in cities. Critical here is the confusion often found concerning property values and the distinction between land and improvements, the latter most often constituted by buildings, where buildings quite naturally can be treated as capital, while land cannot. Importantly, while property value can be increased by its owner through improvements, such as new buildings, she is very limited in influencing the land value, since this is a collective variable dependent on the economic development of the city as a whole. It is here proposed that improvements on land in contemporary urbanised economies to a dominant degree concern systems of centrality and accessibility generating relative locations, that are further enhanced by buildings and land division, and that this constitutes what is proposed to be called a spatial capital, which to a large degree is created through the practices of urban planning and design.In this paper we investigate the dependency of spatial form on land value. First, we review how spatial form and the configurations of accessibility it generates on land, influences housing prices to find support for the intimate relationship between relative location and monetary market values. Second, we investigate the dominance of land values compared to improvement values in four Swedish cities of different size Third, we investigate how known parameters of spatial form correlates with land values in Gothenburg, Sweden. We see close associations between spatial form and land values, both in shape of market housing prices and as property taxation values. Land value holds a larger share of total property taxation value in larger cities, suggesting that relative location is valued higher where economic activity is greater. Furthermore, we find clear correlations between spatial form and land taxation values. Altogether, these findings indicate that spatial capital encompasses monetary value. In extension, these findings also indicate how knowledge based and skilful urban planning and design can create measurable value

The urban economy as a scale-free network

We present empirical evidence that land values are scale-free and introduce a network model that reproduces the observations. The network approach to urban modelling is based on the assumption that the market dynamics that generates land values can be represented as a growing scale-free network. Our results suggest that the network properties of trade between specialized activities causes land values, and likely also other observables such as population, to be power law distributed. In addition to being an attractive avenue for further analytical inquiry, the network representation is also applicable to empirical data and is thereby attractive for predictive modelling.Comment: Submitted to Phys. Rev. E. 7 pages, 3 figures. (Minor typos and details fixed

Networks of urban interaction - Growth and centrality in the complex geography of urban activity

How cities and regions grow and decline depend on technological, social and economic factors. Understanding the interplay of these forces is central in research efforts aiming to improve urban and transport planning. The purpose of this thesis is to explore how mathematical modelling and computer simulation can contribute to these efforts and a central aim is to achieve practically useful models with retained conceptual simplicity as well as correspondence to important empirical patterns.The approach combines a spatially fine-grained representation of land, with processes of urban interaction based on the theory of complex networks. Urban activity at a location is modelled as the sum of all economic interactions stemming from that location. The potentials for interactions and activity are deduced mainly from spatial constraints, such as transport networks and land use regulations. Concepts that are studied include urban growth, accessibility and urban agglomeration.For model validation, an extensive data set on Swedish land taxation values is used. These values are based on actual sales prices and rent levels and can thus be considered as reasonable proxies for urban economic activity. Comparisons are made between empirical data and model outcomes, both with regard to probability distributions and geographical distributions. The empirical probability distribution of land values is found to be well approximated by a power law, strengthening the case for modelling the system as a complex network based on a process of multiplicative growth. By combining these principles with spatial interaction mediated by a transport network, the preferential centrality model is formulated. The activity predictions generated by this model reproduces empirical geographical patterns of land values. The presented models provide explanatory links between the structure of transportation networks and the geographical distributions of urban economic activity. This makes them attractive as starting points for the further step of creating practically useful planning applications. For example, the models could be used to assess how specific transport infrastructure improvements influence urban expansion

Preferential centrality - a new measure unifying urban activity, attraction and accessibility

The fact that accessibility shapes the geographic distribution of activity needs to be addressed in any long-term policy and planning for urban systems. One major problem is that current accessibility measures rely on the identification and quantification of attractions in the system. We propose that it is possible to devise a network centrality measure that bypasses this reliance and predicts the distribution of urban activity directly from the structure of the infrastructure networks over which interactions take place. From a basis of spatial interaction modelling and eigenvector centrality measures we develop what we call a preferential centrality measure that recursively and self-consistently integrates activity, attraction and accessibility. Derived from the same logic as Google’s PageRank algorithm, we may describe its operation by drawing a parallel: Google’s PageRank algorithm ranks the importance of networked documents without the need to perform any analysis of their contents. Instead it considers the topological structure of the network and piggybacks thereby on contextualized and deep evaluation of documents by the myriad distributed agents that constructed the network. We do the same thing with regard to networked geographical zones. Our approach opens up new applications of modelling and promises to alleviate a host of recalcitrant problems, associated with integrated modelling, and the need for large volumes of socioeconomic data. We present an initial validation of our proposed measure by using land taxation values in the Gothenburg municipality as an empirical proxy of urban activity. The resulting measure shows a promising correlation with the taxation values

A complex network approach to urban growth

Economic geography can be viewed as a large and growing network of interacting activities. This fundamental network structure and the large size of such systems makes the complex network approach an attractive model for growth dynamics modeling. In this paper the authors propose the use of complex networks for geographical modeling and demonstrate how such an application can be combined with a cellular model to produce output that is consistent with large-scale regularities such as power laws and fractality. Complex networks can provide a stringent framework for growth dynamic modeling where concepts from, for example, spatial interaction models and multiplicative growth models, can be combined with the flexible representation of land and behaviour found in cellular automata and agent-based models. In addition, there exists a large body of theory for the analysis of complex networks that have direct applications in urban geographic problems. The intended use of such models is twofold: (1) to address the problem of how the empirically observed hierarchical structure of settlements can be explained as a stationary property of a stochastic evolutionary process rather than as equilibrium points in a dynamic process, and, (2) to improve the predictive quality of applied urban modeling.