Mathematical Analysis of Urban Spatial Networks

Blanchard, Philippe; Volchenkov, Dimitri

doi:10.1007/978-3-540-87829-2

Cited by 76 publications

(79 citation statements)

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“…A measure allows seeing a city's map as a "continuous graph" or likewise as an object both relational and geometrical (II). While [3] considered a city as a pure graph and [11] took into account its spatiality, we have explored the geometrical aspect of the city, its topology being only the skeleton that holds it up. From this point of view we have shown that despite an evident diversity on their overall shapes (anisotropy firstorder topology), a few fundamental rules can explain cities' general morphogenesis (IV).…”

Section: Discussionmentioning

confidence: 99%

“…Since the famous "Bridges of Konigsberg" problem by Euler, one is tempted to describe a city as a graph with streets as edges and their intersections as vertices. This provides a relational representation of the city [3]. One of the difficulties then is the particular embedding of these graphs that make random graphs unable to stick to a city's map representation.…”

Section: Introductionmentioning

confidence: 99%

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Mathematics and morphogenesis of cities: A geometrical approach

2011

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Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of the traditional models, from random graphs, complex networks theory, or stochastic geometry, takes into account the geometrical, functional, and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating, and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division or extension of space. We propose a dynamical model that mimics this logic and that, from simple general rules and a few parameters, succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematics and morphogenesis of cities: A geometrical approach

2011

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“…E. g. Volchenkov and Blanchard analyze city structures through random walks to find accessible parts of the city and compare flow-based properties of the graphs to get an understanding on social behavior [18]. An excellent overview on city graphs gives the book by the same authors [19]. Random walks have been studied in many context, a great survey on random walks on graphs is given by Lovász in [14].…”

Section: Related Workmentioning

confidence: 99%

On the impact of graph structure on mobility in opportunistic mobile networks

Mayer

Waldhorst

2011

2011 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)

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Opportunistic mobile networks are a promising way to offload infrastructure networks, or provide communication in case of insufficient or non-existent infrastructure coverage. Understanding of the mobility process that drives such networks is crucial for design, analysis, and configuration. Generally, this mobility process is modeled on a plain playground where devices can move freely; both in case of simulation, and analysis of real-world traces. Graph-based playgrounds provide more realistic models but their impact on mobility is insufficiently understood. We provide a methodology to analyze the impact of the underlying graph on inter-contact time using methods from spectral graph theory. We gather the inter-contact times that both a random and a social mobility model exhibit on synthetic grid-based graphs and real-world city maps through simulations and perform fitting to a model for inter-contact time distribution. We then analyze correlations between parameters of these distributions and the spectral gap of a graph. Our main finding is that the graph structure has strong impact on intercontact time distribution in both random and social mobility on grid-based graphs. For real-world city graphs a social mobility model determines inter-contact time independently of the graph structure, whereas the graph structure has strong impact on inter-contact times for a random mobility process.

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“…12 We require that the main diagonal of the random matrix is 1 and that it is symmetric. 13 Obviously, we have to prevent that the gold standard is ever part of the set of these randomizations. in vector space: the higher the number of indices for which two graphs resemble each other, the more similar the graphs.…”

Section: Module 5: Network Antificationmentioning

confidence: 99%

From Topic Networks to Distributed Cognitive Maps: Zipfian Topic Universes in the Area of Volunteered Geographic Information

et al. 2020

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Are nearby places (e.g. cities) described by related words? In this article we transfer this research question in the eld of lexical encoding of geographic information onto the level of intertextuality. To this end, we explore Volunteered Geographic Information (VGI) to model texts addressing places at the level of cities or regions with the help of so-called topic networks. is is done to examine how language encodes and networks geographic information on the aboutness level of texts. Our hypothesis is that the networked thematizations of places are similar -regardless of their distances and the underlying communities of authors. To investigate this we introduce Multiplex Topic Networks (MTN), which we automatically derive from Linguistic Multilayer Networks (LMN) as a novel model, especially of thematic networking in text corpora. Our study shows a Zip an organization of the thematic universe in which geographical places (especially cities) are located in online communication. We interpret this nding in the context of cognitive maps, a notion which we extend by so-called thematic maps. According to our interpretation of this nding, the organization of thematic maps as part of cognitive maps results from a tendency of authors to generate shareable content that ensures the continued existence of the underlying media. We test our hypothesis by example of special wikis and extracts of Wikipedia. In this way we come to the conclusion: Places, whether close to each other or not, are located in neighboring places that span similar subnetworks in the topic universe.

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Mathematical Analysis of Urban Spatial Networks

Cited by 76 publications

References 0 publications

Mathematics and morphogenesis of cities: A geometrical approach

Mathematics and morphogenesis of cities: A geometrical approach

On the impact of graph structure on mobility in opportunistic mobile networks

From Topic Networks to Distributed Cognitive Maps: Zipfian Topic Universes in the Area of Volunteered Geographic Information

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