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Register a new userScaling Laws in Chennai Bus Network
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In this paper, we study the structural properties of the complex bus network of Chennai. We formulate this extensive network structure by identifying each bus stop as a node, and a bus which stops at any two adjacent bus stops as an edge connecting the nodes. Rigorous statistical analysis of this data shows that the Chennai bus network displays small-world properties and a scale-free degree distribution with the power-law exponent, $gamma > 3$.
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Through the past decade the field of network science has established itself as a common ground for the cross-fertilization of exciting inter-disciplinary studies which has motivated researchers to model almost every physical system as an interacting network consisting of nodes and links. Although public transport networks such as airline and railway networks have been extensively studied, the status of bus networks still remains in obscurity. In developing countries like India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer some of the basic questions on its evolution, growth, robustness and resiliency. In this paper, we model the bus networks of major Indian cities as graphs in textit{L}-space, and evaluate their various statistical properties using concepts from network science. Our analysis reveals a wide spectrum of network topology with the common underlying feature of small-world property. We observe that the networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, like Internet, WWW and airline, which are virtual, bus networks are physically constrained. The presence of various geographical and economic constraints allow these networks to evolve over time. Our findings therefore, throw light on the evolution of such geographically and socio-economically constrained networks which will help us in designing more efficient networks in the future.
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realisations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size regardless of the definition of the urban boundaries. However, when non-linear correlations are present, the exponent fluctuates considerably.
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that is ubiquitous in the real world, and calculate its degree distributions. Our results show that the tails of its degree distributions exhibits a distinct power law feature, providing robust theoretical support for the ubiquity of the power law feature. Second, we suggest that in the real world two important factors, network size and node disappearance probability, point to the existence of the power law feature in the observed networks. As network size reduces, or as the probability of node disappearance increases, then the power law feature becomes increasingly difficult to observe. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behaviour of the degree distribution within its effective intervals.
Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social networks have been studied extensively. Many important universal properties with which we are quite familiar have been recovered, such as scale free degree distribution, small world, community structure, self-similarity and navigability. According to some empirical investigations, we conclude that our social network also possesses another important universal property. The spatial structure of social network is scale invariable. The distribution of geographic distance between friendship is about $Pr(d)propto d^{-1}$ which is harmonious with navigability. More importantly, from the perspective of searching information, this kind of property can benefit individuals most.
We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate $lambda_c$ at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold that could potentially serve as early-warning signs. These measures include the $SI$ link density, triplet densities, clustering, assortativity and the eigenvalue gap. For the $SI$ link density and triplet densities the maximum is found to originate from the co-existence of two power laws. Other network quantities, such as the degree, the branching ratio, or the harmonic mean distance, show scaling with a singularity at $lambda=0$ and not at $lambda_c$, which means that they are incapable of detecting the transition.
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