title: Extraction of conjugate main-stream structures from a complex network flow.
abstract: We introduce a method to extract main-stream structures for a given complex network flow by trimming less effective links. As the resulting main streams generally have an almost loopless treelike structure, we can define the stream basin size for each node, which characterizes the importance of the node with regard to the flow. As a real-world example, we apply this method to an interfirm trading network, both for the money flow and its conjugate-the material or service flow-confirming that both basin size distributions follow a similar power law that differs significantly from the basin size distributions of rivers in nature. We theoretically analyze the process of trimming and derive a consistent statistical formulation between the original link number and the basin size.
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G3-52 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan.
authors.forename: Koutarou
authors.initials: K
authors.lastname: Tamura
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G3-52 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan.|Sony Computer Science Laboratories, 3-14-13 Higashigotanda, Shinagawa-ku, Tokyo 141-0022, Japan.|Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan.
authors.forename: Hideki
authors.initials: H
authors.lastname: Takayasu
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G3-52 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan.
authors.forename: Misako
authors.initials: M
authors.lastname: Takayasu