Structural properties of planar graphs of urban street patterns

Cardillo, Alessio; Scellato, Salvatore; Latora, Vito; Porta, Sergio

doi:10.1103/physreve.73.066107

Cited by 306 publications

(317 citation statements)

References 32 publications

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“…[9][10][11]. Several studies have computed graph measures and used them to quantify the local and large scale organization of real world spatial patterns, such as urban street patterns [12][13][14][15][16][17][18][19][20], systems of animal trails [21] and galleries [22][23][24][25][26], networks of channels in trabecular bones [27,28], networks of fungal hyphae [29].…”

Section: Introductionmentioning

confidence: 99%

Characterization of spatial networklike patterns from junction geometry

2011

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We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely topological estimators: also patterns that both look different and result from different morphogenetic processes can have similar topology. A local geometric cue -the angles formed by the different branches at junctions-can complement topological information and allow to quantify the large scale spatial coherence of the pattern. For patterns that grow over time, such as fracture lines on the surface of ceramics, the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment. We apply the method to various network-like patterns and we find a continuous but sharp dichotomy between two classes of spatial networks: hierarchical and homogeneous. The first class results from a sequential growth process and presents large scale organization, the latter presents local, but not global organization.

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Section: Introductionmentioning

confidence: 99%

Characterization of spatial networklike patterns from junction geometry

2011

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“…While the case of San Joaquin (panel C) evidences a scaling regime with a correlation dimension converging to 2 (β = 1.83 ± 0.1 for m = 3), no scaling is found for the self-organized city of Oldenburg (panel D), suggesting that this latter network does not possess a well defined dimension. These different behaviors deepen on the recently observed structural differences between cities that have grown according to different evolutionary mechanisms [31,32]. In the Supplemental Material [33] we include additional analysis and estimation of the correlation dimension of other real world examples including technological (Internet at the Autonomous System level [34] and the Italian power grid [35]) and road (San Francisco [29] and USA [36]) networks.…”

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confidence: 99%

Correlation Dimension of Complex Networks

Lacasa

Gómez‐Gardeñes

2013

Phys. Rev. Lett.

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We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers. Preprint version merging the main article and the supplementary material. To be published in Physical Review Letters.PACS numbers: 05.45. Ac,89.75.Fb Network science has influenced the recent progress in many areas of statistical and nonlinear physics [1]. The discovery of the real architecture of interactions of many systems studied under the former disciplines [2-4] changed the usual mean-field way to tackle problems arising in sociology, biology, epidemiology and technology among others [5]. Furthermore, the blossom of the network theoretical machinery [6], has provided a forefront framework to interpret the relations encoded in large datasets of diverse nature and fostered the application of new techniques, such as community detection algorithms [7], to coarse-grain the complex and hierarchical landscape of interactions of real-world systems.Recently, geometrical concepts have been exploited to describe and classify the structure of complex networks beyond purely topological aspects [8][9][10][11]. In particular, the box-counting technique, widely used for estimating the capacity dimension D 0 of an object, has been recently extended, as a box-covering algorithm, to characterize the dimensionality of complex networks [11][12][13][14]. This technique proceeds by calculating the number N of boxes of Euclidean volume L d required to cover an object, being the capacity dimension D 0 of such object given by D 0 = lim L→0 log N log(1/L) . The capacity dimension D 0 is thus seen as an upper bound to the Hausdorff dimension.The box-covering approach, while being the most natural and elegant extension of the concept of fractal dimension to networks, suffers from some difficulties. First, in order to tile the network and to unambiguosly relate the box-covering and capacity dimensions, the object under study must be embedded in a metric space, something that does not apply in the more general case of a complex network. This subtle problem can be overcome by restricting to spatially embedded complex networks [14]. A second important issue is the need of full knowledge of the network topology in order to perform the box-covering procedure. This constraint faces the limitations related to storing the complete network backbone, indeed, the computation of the capacity dimension becomes unpractical for embedding dimensions larger than 3 [15]. Finally, another related problem is tha...

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“…Characteristics of real-world networks are essential to evaluate past developments. For example, Cardillo et al (2006) and Strano et al (2012) evaluated real-world networks and past network developments such as densities and lengths. However, the main focus of this paper relies on artificially generated networks and network models.…”

Section: Objective and Application Specificationsmentioning

confidence: 99%

Shape grammars overview and assessment for transport and urban design: Review, terminology, assessment, and application

Vitins

Axhausen²

2016

JTLU

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Shape grammars for urban design have attracted much interest in research and practice. Transport and urban planners increasingly deploy shape grammars, especially in simulations and procedural models. Shape grammars have multiple advantages due to their interdisciplinary and straightforward approach and low computational requirements. In addition, a rulebased design method and underlying fundamental research knowledge can potentially support future planning and design guidelines for handbooks and norms. However, little is known about the effectiveness of shape grammars in transport networks and urban environments. e proposed methodology aims at a future development of a robust and effective language for sustainable urban development. e theory of different fields is consolidated for a general grammar definition. Grammars require specified and corresponding objectives and application specifications for enhanced implementation. e proposed methodology for grammar rule assessment is based on elasticities to gain more insights in the effect of the rules. Elasticities allow comprehensive comparisons and verification between grammar rules. e paper reviews and highlights the key achievements and applications of shape grammars in cognate fields of science. Terminology sheds light on the definitions of most relevant terms including a general definition for grammar rules embedded in the language context. e paper differentiates methodological approaches in grammar design assessment and emphasizes a standardized approach for shape grammar definitions. e paper concludes with a detailed example for grammar rule assessment and potential future research.

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Structural properties of planar graphs of urban street patterns

Cited by 306 publications

References 32 publications

Characterization of spatial networklike patterns from junction geometry

Characterization of spatial networklike patterns from junction geometry

Correlation Dimension of Complex Networks

Shape grammars overview and assessment for transport and urban design: Review, terminology, assessment, and application

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