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      Statistical Analysis of Bus Networks in India

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      PLoS ONE
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          Abstract

          In this paper, we model the bus networks of six major Indian cities as graphs in L-space, and evaluate their various statistical properties. While 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 transport plays an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer basic questions on its evolution, growth, robustness and resiliency. Although the common feature of small-world property is observed, our analysis reveals a wide spectrum of network topologies arising due to significant variation in the degree-distribution patterns in the networks. We also observe that these networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, such as Internet, WWW and airline, that are virtual, bus networks are physically constrained. Our findings therefore, throw light on the evolution of such geographically and constrained networks that will help us in designing more efficient bus networks in the future.

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          Most cited references6

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          Emergence of scaling in random networks

          Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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            Lethality and centrality in protein networks

            In this paper we present the first mathematical analysis of the protein interaction network found in the yeast, S. cerevisiae. We show that, (a) the identified protein network display a characteristic scale-free topology that demonstrate striking similarity to the inherent organization of metabolic networks in particular, and to that of robust and error-tolerant networks in general. (b) the likelihood that deletion of an individual gene product will prove lethal for the yeast cell clearly correlates with the number of interactions the protein has, meaning that highly-connected proteins are more likely to prove essential than proteins with low number of links to other proteins. These results suggest that a scale-free architecture is a generic property of cellular networks attributable to universal self-organizing principles of robust and error-tolerant networks and that will likely to represent a generic topology for protein-protein interactions.
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              Assortative mixing in networks

              M. Newman (2002)
              A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2016
                19 December 2016
                : 11
                : 12
                : e0168478
                Affiliations
                [001]Department of Civil Engineering, Indian Institute of Technology Madras, Chennai-600036, India
                Universidad Rey Juan Carlos, SPAIN
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                • Conceptualization: AC GR.

                • Data curation: AC MM.

                • Formal analysis: AC GR.

                • Funding acquisition: GR.

                • Investigation: AC MM.

                • Methodology: AC GR MM.

                • Project administration: GR.

                • Resources: GR.

                • Software: AC.

                • Supervision: GR.

                • Validation: AC GR.

                • Visualization: AC.

                • Writing – original draft: AC MM.

                • Writing – review & editing: AC GR.

                [¤]

                Current address: Department of Physics, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, United States of America

                Author information
                http://orcid.org/0000-0002-1787-9838
                Article
                PONE-D-16-20823
                10.1371/journal.pone.0168478
                5167384
                27992590
                9a29c743-1166-498e-9197-b1efa31bef6e
                © 2016 Chatterjee et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 23 May 2016
                : 29 November 2016
                Page count
                Figures: 6, Tables: 1, Pages: 16
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100001855, Ministry of Urban Development;
                Award Recipient :
                Funded by: Information Technology Research Academy, Media Labs India
                Award Recipient :
                The authors acknowledge the support from Center of Excellence in Urban Transport at the Indian Institute of Technology, Madras, sponsored by the Ministry of Urban Development, Government of India and the Information Technology Research Academy, a Division of Media Labs Asia, a non-profit organization of the Department of Electronics and Information Technology, funded by the Ministry of Communications and Information Technology, Government of India. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Computer and Information Sciences
                Network Analysis
                Computer and Information Sciences
                Network Analysis
                Centrality
                Computer and Information Sciences
                Network Analysis
                Scale-Free Networks
                Computer and Information Sciences
                Data Visualization
                Infographics
                Graphs
                Engineering and Technology
                Transportation
                Computer and Information Sciences
                Network Analysis
                Protein Interaction Networks
                Biology and Life Sciences
                Biochemistry
                Proteomics
                Protein Interaction Networks
                Computer and Information Sciences
                Network Analysis
                Social Networks
                Social Sciences
                Sociology
                Social Networks
                Engineering and Technology
                Structural Engineering
                Built Structures
                Custom metadata
                All data files are available at https://github.com/achatterjee3/Dataset.

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