Power law and small world properties in a comparison of traffic city networks

Ma, Ke; Wang, ZhongWen; Jian, Jiang; Zhu, Guangxi; Li, Wei

doi:10.1007/s11434-011-4769-4

Cited by 15 publications

(6 citation statements)

References 54 publications

(53 reference statements)

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“…The presence of more hubs in the Beijing network yielded a smaller γ as compared to Chengdu; while both showed large clustering coefficients and small characteristic path lengths. The location of bus stops in a similar fashion in both the cities have led to a hierarchical structure, which is denoted by a power-law behaviour (with nearly same exponents) between the degree strength (characterizing the passenger flows) and clustering coefficient [53,54].…”

Section: Studies On Bus Transport Networkmentioning

confidence: 99%

Studies on the Structure and Dynamics of Urban Bus Networks in Indian Cities

Chatterjee¹

2015

Preprint

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In recent times, the domain of network science has become extremely useful in understanding the underlying structure of various real-world networks and to answer non-trivial questions regarding them. In this study, we rigourously analyze the statistical properties of the bus networks of six major Indian cities as graphs in L-and P -space, using tools from network science. Although public transport networks, such as airline and railway networks have been extensively studied, a comprehensive study on the structure and growth of bus networks is lacking. In India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze their topological structure, and answer some of the basic questions on their evolution, growth, robustness and resiliency. We start from an empirical analysis of these networks, and determine their principle characteristics in terms of the complex network theory. The common features of small-world property and heavy tails in degree-distribution plots are observed in all the networks studied. Our analysis further reveals a wide spectrum of network topologies arising due to an interplay between preferential and random attachment of nodes. Unlike real-world networks, like the Internet, WWW and airline, which are virtual, bus networks are physically constrained in two-dimensional space by the underlying road networks. In order to understand the role of constraints in the evolution of these networks, we calculate their fractal dimensions that reveal a three-dimensional space-like evolution in a constrained two-dimensional plane. We also extend our study to understand the complex dynamical processes of epidemic outbreaks and information diffusion in these networks using SI and SIR models. Our findings, therefore throw light on the evolution and dynamics of such geographically and socio-economically constrained networks, which will help us in designing more efficient networks in the future.

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Section: Studies On Bus Transport Networkmentioning

confidence: 99%

Studies on the Structure and Dynamics of Urban Bus Networks in Indian Cities

Chatterjee¹

2015

Preprint

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“…Traditional modeling approaches to illness propagations, such as COVID-19, assume an exponential growth ( Chen et al, 2020 ; Liang, 2020 ; Liu et al, 2020 ; Pinter et al, 2020 ; Santosh, 2020 ; Shinde et al, 2020 ). However, increasing evidence shows that human dynamics have power-law properties ( Barabási, 2007 ; Grabowski, 2007 ; Ma et al, 2011 ; Muchnik et al, 2013 ). In fact, recent work has shown that multiple measurements of human activity follow allometric properties such as

, where N is the number of individuals and w a metric of activity ( Bettencourt et al, 2010 ).…”

Section: Introductionmentioning

confidence: 99%

The allometric propagation of COVID-19 is explained by human travel

Tuladhar

Grigolini

Santamarı́a

2022

Infectious Disease Modelling

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We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, and even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles traveled in the US. Together, air and vehicular travel explained 70% of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

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“…Traditional modeling approaches to illness propagations, such as COVID-19, assume an exponential growth (11)(12)(13)(14)(15)(16). However, increasing evidence shows that human dynamics and clustering has power-law properties (17)(18)(19)(20). In fact, recent work has shown that multiple measurements of human activity follow allometric properties such as ∝ , where N is the number of individuals and w a metric of activity (21).…”

Section: Introductionmentioning

confidence: 99%

The allometric propagation of COVID-19 is explained by human travel

Tuladhar

Grigolini

Santamarı́a

2021

Preprint

View full text Add to dashboard Cite

We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, an even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles travelled in the US. Together, air and vehicular travel explained 70 % of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

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Power law and small world properties in a comparison of traffic city networks

Cited by 15 publications

References 54 publications

Studies on the Structure and Dynamics of Urban Bus Networks in Indian Cities

Studies on the Structure and Dynamics of Urban Bus Networks in Indian Cities

The allometric propagation of COVID-19 is explained by human travel

The allometric propagation of COVID-19 is explained by human travel

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