José Luis Oliver

An algorithm for ranking the nodes of an urban network based on the concept of PageRank vector

Abstract This paper presents a new method to establish a ranking of nodes in an urban network. In the original PageRank algorithm, a single PageRank vector is computed to determine the relative importance of Web pages, independent of any particular search query. We follow a similar reasoning, adapting the concept of PageRank vector to urban networks. We translate an urban network to graph theory language, where the nodes represent crossings or squares and the edges represent the connections between nodes. In this scenario, our main goal is to establish a ranking of importance of the different nodes in the graph. Unlike the PageRank model which only takes into account the connections between the Web pages, in our method we must consider other external factors to carry out the classification. These external factors may have some characteristics associated with the nodes and they are different according to the problem we are working. These characteristics are usually related to the presence of some facilities or endowments in the nodes of the network, like for example the presence of restaurants, bars, shopping centers, stores, and so on. A data matrix will collect the quantification of each of the characteristics studied for each node and will play an important role in the process of classification. Considering the influence of all these characteristics, we construct a matrix with some interesting algebraic features which allow us to compute an eigenvector associated to the dominant eigenvalue λ = 1 . This vector constitutes the solution to our problem of ranking the nodes of the network. The model is applied to a real example, in which we consider a part (the old town) of the city of Murcia (Spain). For this example, we apply the PageRank model, as well as the proposed model in this paper, in order to perform a comparative study of both models. This example clearly shows the importance of considering external factors to quantify the urban network nodes.

Analyzing the commercial activities of a street network by ranking their nodes: a case study in Murcia, Spain

Urban researchers and planners are often interested in understanding how economic activities are distributed in urban regions, what forces influence their special pattern and how urban structure and functions are mutually dependent. In this paper, we want to show how an algorithm for ranking the nodes in a network can be used to understand and visualize certain commercial activities of a city. The first part of the method consists of collecting real information about different types of commercial activities at each location in the urban network of the city of Murcia, Spain. Four clearly differentiated commercial activities are studied, such as restaurants and bars, shops, banks and supermarkets or department stores, but obviously we can study other. The information collected is then quantified by means of a data matrix, which is used as the basis for the implementation of a PageRank algorithm which produces a ranking of all the nodes in the network, according to their significance within it. Finally, we visualize the resulting classification using a colour scale that helps us to represent the business network.

An application of a self-organizing model to the design of urban transport networks

A 2D triangle mesh simplification model is described in this paper, with the main objective of preserving the shape of the original mesh. The proposed model consists of a self-organizing algorithm whose objective is to generate the positions of the nodes of the simplified mesh; afterwards, a triangulation algorithm is performed to reconstruct the triangles of the new simplified mesh. The self-organizing algorithm is an unsupervised learning algorithm that provides a set of nodes representing the best approximation of the original mesh. An adaptation of the neural network algorithm is proposed with the primary objective to work in the context of urban transport networks. We verify the effectiveness of this model through the design and development of some urban network problems. Specifically, the algorithm is applied to two real problems, the first one is the design of a tramway network in a town, and the second one is the design of an information point network within a real bus transport network.

A Model to Visualize Information in a Complex Streets' Network

This paper discusses a process to graphically view and analyze information obtained from a network of urban streets, using an algorithm that establishes a ranking of importance of the nodes of the network itself. The basis of this process is to quantify the network information obtained by assigning numerical values to each node, representing numerically the information. These values are used to construct a data matrix that allows us to apply a classification algorithm of nodes in a network in order of importance. From this numerical ranking of the nodes, the process finish with the graphical visualization of the network. An example is shown to illustrate the whole process.

A neural network model to develop actions in urban complex systems represented by 2D meshes

The main idea of this work is to present a tool which may be useful to generate a mesh of points where urban actions may be taken after analysing and understanding complex urban situations. By the word complex we mean urban concentrations without precise limits and without a recognizable geometry pattern. In these situations, it is very hard for the architects to understand the system. Therefore, it is very difficult to define an action plan for this type of urban situations. What we propose is an adaptation of a neural network algorithm to work in the context of urban networks. Our objective is to develop a strategy to change this weakness of sparse urban development by activating public spaces with new meanings. A new 2D triangle mesh simplification model is introduced with the central property of preserving the shape of the original mesh. The mathematical model presented consists of a self-organizing algorithm whose objective is to generate the positions of the nodes of the simplified mesh; afterwards, a triangulation algorithm is carried out to reconstruct the triangles of the new simplified mesh. With this algorithm, it is possible to perform specific actions in an urban space, because the urban territory can be considered as a complex mesh with nodes and edges. A real example of an urban action is shown with the introduction of a wireless network in a residential area.

Reducing Urban Concentration Using a Neural Network Model

We present a 2D triangle mesh simplification model, which is able to produce high quality approximations of any original planar mesh, regardless of the shape of the original mesh. This model is applied to reduce the urban concentration of a real geographical area, with the property to maintain the original shape of the urban area. We consider the representation of an urbanized area as a 2D triangle mesh, where each node represents a house. In this context, the neural network model can be applied to simplify the network, what represents a reduction of the urban concentration. A real example is detailed with the purpose to demonstrate the ability of the model to perform the task to simplify an urban network.

A neural network model to develop urban acupuncture

The urban world of the 21st century is composed of numerous nodes, streams and webs, which create a new landscape of globalization and impose different logic of space and time perception. Therefore, the urban infrastructure is updated and its networks are continuously multiplied. A method known as urban acupuncture on the one hand tests the local effects of every project, and on the other hand establishes a network of points or dots to act upon. The main objective of this paper is to relate the concept of urban acupuncture with the use of a neural network algorithm to determine those points where developing actions in order to improve the quality life in cities. We apply the neural network model GNG3D to the design of a simplified network in a real city of our surrounding.

Quantification and Visualization of a Heritage Conservation in a Quito Neighbourhood (Ecuador)

This paper focuses on the process of quantification and visualization of a heritage conservation study in a neighbourhood of Quito (Ecuador). The first part of the paper consists of collecting real information about different features of every building in the urban network of the mentioned neighbourhood. The information collected is then quantified by means of a data matrix that allows us to obtain an indicator of the heritage conservation of every parcel studied. In order to better understand the preservation of the neighbourhood, an analysis and visualization of the obtained indicators is carried out. The visualization is based on a non-linear interpolation of the vertices of a grid using a chromatic scale. This type of visualization provides a smooth graphic that helps us to represent areas that are more or less interesting from the point of view of the heritage conservation state.

Different Types of Graphs to Model a City

This work was partially supported by the Spanish Government, Ministerio de Economia y Competividad, which reference number is TIN2014-53855-P.

Analysis of the Patrimonial Conservation of a Quito Suburb without Altering Its Commercial Structure by Means of a Centrality Measure for Urban Networks

In about 1940, Quito’s urban planning department contemplated the creation of a new suburb called Villaflora following the garden city model: homes in connection with nature but also near services. In Villaflora we do not find monumental elements that characterize patrimonial architecture; the value of Villaflora’s patrimony is in its urban model characterized by some architectonic elements. However, Villaflora is valuable because it is the result of a unique urban model. Over the years, the suburb has suffered profound degradation from the point of view of its patrimonial conservation. Hence, we propose an urban intervention in the suburb that contemplates the restoration of some important elements in the urban layout, without altering the commercial structure of the same. To accomplish this task we perform a study of the heritage conservation of each of the buildings of the suburb, as well as a study of the commercial activity that is developed in the suburb in order to determine those areas with the highest commercial activity and as a consequence, a greater presence of people in the streets and public spaces.