Scaling Laws in Chennai Bus Network

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, = 3:8. I. INTRODUCTION A. Chennai Bus Network Chennai is one of the metropolitan cities in India with a structured and a close-knit bus transport network. The Chennai bus network (CBN) is operated by the Metropolitan Transport Corporation (MTC), a state government undertaking. Spanning an area of 3,929 sq. km and with over 800 routes sprawling across entire Chennai, this extensive network also boasts of the largest bus terminus in Asia. With the population of the city being the sixth largest in the country, this medium of transport is most widely used for day-to-day commutation. The reason that the bus network, in general, achieves this favourable status lies primarily in two factors: (i) cost, and (ii) penetration. With high volume of commuters flowing through this network each day, the cost of travel per day, per person becomes significantly low. Although, this is a parameter which is usually met by every other public transport system, the penetration factor is the one which significantly makes bus networks the prime mode of transportation in cities. A high penetration effect exhibited by a bus network enables a person to travel between any two points in the city very easily which is in contrast to other public modes of transportation, where geographical constraints associated with the network layout are much higher in number. Thus, bus transportation allows flexibility in travel. A natural question arises here; what is the least number of buses one should change to go from one place to another? Or more precisely, why do we require changing buses at all? To answer these questions, we need to look at a more abstract and networked structure of the bus routes, and argue based on its various statistical properties. B. Complex Networks: overview

[1]  Arun K. Ramani,et al.  Protein interaction networks from yeast to human. , 2004, Current opinion in structural biology.

[2]  R. N. Onody,et al.  Complex network study of Brazilian soccer players. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Ricard V. Solé,et al.  Least effort and the origins of scaling in human language , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Alessandro Vespignani,et al.  EPIDEMIC SPREADING IN SCALEFREE NETWORKS , 2001 .

[5]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[6]  Ziyou Gao,et al.  URBAN TRANSIT SYSTEM AS A SCALE-FREE NETWORK , 2004 .

[7]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[8]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Ganesh Bagler,et al.  Analysis of the airport network of India as a complex weighted network , 2004, cond-mat/0409773.

[10]  E. David,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World , 2010 .

[11]  Réka Albert,et al.  Structural vulnerability of the North American power grid. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[13]  Alex Arenas,et al.  Traffic-driven epidemic spreading in finite-size scale-free networks , 2009, Proceedings of the National Academy of Sciences.

[14]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[15]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[16]  J. Hołyst,et al.  Statistical analysis of 22 public transport networks in Poland. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[18]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[19]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[20]  Henry G. Small,et al.  Co-citation in the scientific literature: A new measure of the relationship between two documents , 1973, J. Am. Soc. Inf. Sci..

[21]  Arnab Chatterjee,et al.  Small-world properties of the Indian railway network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Sybil Derrible,et al.  The complexity and robustness of metro networks , 2010 .

[23]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[24]  V. Palchykov,et al.  Public transport networks: empirical analysis and modeling , 2008, 0803.3514.

[25]  Xin-She Yang,et al.  Small‐world networks in geophysics , 2001, 1003.4886.

[26]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[27]  Xinping Xu,et al.  Scaling and correlations in three bus-transport networks of China , 2007, 0708.2606.

[28]  S. Havlin,et al.  Scale-free networks are ultrasmall. , 2002, Physical review letters.

[29]  Lei Wang,et al.  Robustness Measure of China’s Railway Network Topology Using Relative Entropy , 2013 .

[30]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[31]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[32]  B. Bollobás.  The evolution of random graphs , 1984 .

[33]  Christian Biemann,et al.  Chinese Whispers - an Efficient Graph Clustering Algorithm and its Application to Natural Language Processing Problems , 2006 .