Topological Analysis of Urban Street Networks

10.1068/b306 ◽  
2004 ◽  
Vol 31 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Bin Jiang ◽  
Christophe Claramunt
Keyword(s):  
Topological Analysis ◽  
Small World ◽  
Clustering Coefficient ◽  
Graph Representation ◽  
Small World Networks ◽  
Street Network ◽  
Scale Free ◽  
Urban Street ◽  
Street Networks ◽  
Functional Graph

The authors propose a topological analysis of large urban street networks based on a computational and functional graph representation. This representation gives a functional view in which vertices represent named streets and edges represent street intersections. A range of graph measures, including street connectivity, average path length, and clustering coefficient, are computed for structural analysis. In order to characterise different clustering degrees of streets in a street network they generalise the clustering coefficient to a k-clustering coefficient that takes into account k neighbours. Based on validations applied to three cities, the authors show that large urban street networks form small-world networks but exhibit no scale-free property.

scholarly journals On the Influence of Topological Characteristics on Robustness of Complex Networks

2013 ◽  
Vol 3 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Dharshana Kasthurirathna ◽  
Mahendra Piraveenan ◽  
Gnanakumar Thedchanamoorthy
Keyword(s):  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Scale Free ◽  
Rich Club ◽  
Targeted Attacks ◽  
Topological Characteristics ◽  
Topological Robustness

Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.

scholarly journals On equilibrium Metropolis simulations on self-organized urban street networks

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Jérôme G. M. Benoit ◽  
Saif Eddin G. Jabari
Keyword(s):  
State Of The Art ◽  
Small World ◽  
Metropolis Algorithm ◽  
The State ◽  
Scale Free ◽  
Urban Street ◽  
Amount Of Information ◽  
Street Networks ◽  
Self Organized ◽  
Wide Range

AbstractUrban street networks of unplanned or self-organized cities typically exhibit astonishing scale-free patterns. This scale-freeness can be shown, within the maximum entropy formalism (MaxEnt), as the manifestation of a fluctuating system that preserves on average some amount of information. Monte Carlo methods that can further this perspective are cruelly missing. Here we adapt to self-organized urban street networks the Metropolis algorithm. The “coming to equilibrium” distribution is established with MaxEnt by taking scale-freeness as prior hypothesis along with symmetry-conservation arguments. The equilibrium parameter is the scaling; its concomitant extensive quantity is, assuming our lack of knowledge, an amount of information. To design an ergodic dynamics, we disentangle the state-of-the-art street generating paradigms based on non-overlapping walks into layout-at-junction dynamics. Our adaptation reminisces the single-spin-flip Metropolis algorithm for Ising models. We thus expect Metropolis simulations to reveal that self-organized urban street networks, besides sustaining scale-freeness over a wide range of scalings, undergo a crossover as scaling varies—literature argues for a small-world crossover. Simulations for Central London are consistent against the state-of-the-art outputs over a realistic range of scaling exponents. Our illustrative Watts–Strogatz phase diagram with scaling as rewiring parameter demonstrates a small-world crossover curving within the realistic window 2–3; it also shows that the state-of-the-art outputs underlie relatively large worlds. Our Metropolis adaptation to self-organized urban street networks thusly appears as a scaling variant of the Watts–Strogatz model. Such insights may ultimately allow the urban profession to anticipate self-organization or unplanned evolution of urban street networks.

Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains

2013 ◽  
Vol 110 (10) ◽  
Author(s):  
Ralph Stoop ◽  
Victor Saase ◽  
Clemens Wagner ◽  
Britta Stoop ◽  
Ruedi Stoop
Keyword(s):  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Cortical Columns

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

scholarly journals Quantitative method for resilience assessment framework of airport network during COVID-19

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260940
Author(s):  
Jiuxia Guo ◽  
Yang Li ◽  
Zongxin Yang ◽  
Xinping Zhu
Keyword(s):  
Complex Network ◽  
Small World ◽  
Global Scale ◽  
Assessment Framework ◽  
Small World Networks ◽  
Scale Free ◽  
Global Pandemic ◽  
Network Metrics ◽  
Resilience Assessment

The resilience and vulnerability of airport networks are significant challenges during the COVID-19 global pandemic. Previous studies considered node failure of networks under natural disasters and extreme weather. Herein, we propose a complex network methodology combined with data-driven to assess the resilience of airport networks toward global-scale disturbance using the Chinese airport network (CAN) and the European airport network (EAN) as a case study. The assessment framework includes vulnerability and resilience analyses from the network- and node-level perspectives. Subsequently, we apply the framework to analyze the airport networks in China and Europe. Specifically, real air traffic data for 232 airports in China and 82 airports in Europe are selected to form the CAN and EAN, respectively. The complex network analysis reveals that the CAN and the EAN are scale-free small-world networks, that are resilient to random attacks. However, the connectivity and vulnerability of the CAN are inferior to those of the EAN. In addition, we select the passenger throughput from the top-50 airports in China and Europe to perform a comparative analysis. By comparing the resilience evaluation of individual airports, we discovered that the factors of resilience assessment of an airport network for global disturbance considers the network metrics and the effect of government policy in actual operations. Additionally, this study also proves that a country’s emergency response-ability towards the COVID-19 has a significantly affectes the recovery of its airport network.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

Complex Systems in a Nutshell

2020 ◽  
pp. 19-32
Author(s):  
Megan S. Patterson ◽  
Michael K. Lemke ◽  
Jordan Nelon
Keyword(s):  
Complex Systems ◽  
Path Length ◽  
Path Dependence ◽  
Small World ◽  
Cardiometabolic Disease ◽  
Small World Networks ◽  
Stable States ◽  
Scale Free ◽  
Critical Transitions ◽  
Random Scale

This chapter provides an overview of the key foundational concepts and principles of the study of complex systems. First, a definition for system is provided, and the distinctions between complicated and complex systems are demarcated, as are detail, disorganized, organized, and dynamic types of complexity. Common properties across complex systems are defined and described, including stable states and steady states, path dependence, resilience, critical transitions and tipping points, early warning signals, feedback loops, and nonlinearity. This chapter also delves into how complex issues often consist of networks, with random, scale-free, and small world networks defined and network concepts such as degrees, path length, and heterogeneity defined. The concept of emergence is also emphasized, as well as related principles such as adaptation and self-organization. Cardiometabolic disease (and associated comorbidities) is used in this chapter as a thematic population health example.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

The Development of Pompeii’s Urban Street Network

2017 ◽  
Author(s):  
Eric E. Poehler
Keyword(s):  
Urban Form ◽  
Formal Analysis ◽  
Street Network ◽  
Urban Street ◽  
Street Networks ◽  
The City ◽  
Present Understanding

Chapter 2 explores the present understanding of Pompeii’s evolution by disassembling the apparent patchwork of grids across the city and reconsiders the presumed awkwardness in their adhesion. To do this, the traditional tools of formal analysis—street alignments and block shapes—are employed with and critiqued by the stratigraphic evidence recovered in the last three decades of excavation below the 79 CE levels. The result is an outline of the development of Pompeii’s urban form as a series of street networks: from the archaic age, through the period of the “hiatus” of the fifth and fourth centuries BCE, to a reorganization of the city’s space so profound that it can genuinely be considered a refoundation, and finally to the adjustments of a refounded city in the Colonial, Augustan, and post-earthquake(s) periods.

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