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Scale-free property of directed networks with two intrinsic node weights

Author

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  • Shioda, Shigeo
  • Nakamura, Kazuhiro

Abstract

This paper proposes a network model to understand the scale-free property of directed networks. The proposed model assigns two intrinsic variables (incoming and outgoing weights) to every node. A directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold. The proposed model allows us to know the exact analytical expressions for degree distributions and clustering. We analytically find that the in-degree and out-degree distributions have power-law tails and their scaling exponents are controllable within the range (1,∞). The average clustering coefficient of nodes with out-degree (or in-degree) n also has a power-law tail as a function of n. We also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights.

Suggested Citation

  • Shioda, Shigeo & Nakamura, Kazuhiro, 2009. "Scale-free property of directed networks with two intrinsic node weights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3249-3260.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:15:p:3249-3260
    DOI: 10.1016/j.physa.2009.04.018
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    References listed on IDEAS

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    1. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
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