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Double Power-Law Degree Distribution And Informational Entropy In Urban Road Networks

Author

Listed:
  • JIAN JIANG

    (Complexity Science Center, Institute of Particle Physics, Hua-Zhong (Central China), Normal University, Wuhan 430079, China;
    Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France;
    LPEC, Faculté des Sciences et Techniques, Université du Maine, Ave. O. Messiaen, 72035 Le Mans, France)

  • FRÉDÉRIC METZ

    (Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France)

  • CHRISTOPHE BECK

    (Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France)

  • SÉBASTIEN LEFEVRE

    (Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France)

  • JINCAN CHEN

    (Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France;
    Department of Physics, Xiamen University, Xiamen 361005, China)

  • QIUPING A. WANG

    (Institut Supérieur des Matériaux et Mécaniques Avancés, 44, Avenue F. A. Bartholdi, 72000 Le Mans, France;
    LPEC, Faculté des Sciences et Techniques, Université du Maine, Ave. O. Messiaen, 72035 Le Mans, France)

  • MICHEL PEZERIL

    (LPEC, Faculté des Sciences et Techniques, Université du Maine, Ave. O. Messiaen, 72035 Le Mans, France)

Abstract

The double power-law function,p(x) ~ 1/(xb+ cxd)wherexis the degree of one node, andb,c,dare parameters, is used to fit the degree distribution of urban road network of Le Mans city in France. It is called "double power-law" since it behaves as two power laws respectively, in large and small degree region with a crossing in-between. The position of the crossing point is derived as a function of the three parameters. The probabilistic uncertainty of this law is studied with two possible information measures: a generalized measure called varentropy and the Shannon entropy formula.

Suggested Citation

  • Jian Jiang & Frédéric Metz & Christophe Beck & Sébastien Lefevre & Jincan Chen & Qiuping A. Wang & Michel Pezeril, 2011. "Double Power-Law Degree Distribution And Informational Entropy In Urban Road Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 13-20.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:01:n:s0129183111016075
    DOI: 10.1142/S0129183111016075
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