Diffusion-localization transition caused by nonlinear transport on complex networks.

We analyzed nonlinear transport as defined for directed complex networks, where the flux from one node to a neighboring node is given preferentially according to the scalar quantities at the neighbor nodes. This is known as the generalized gravity interaction. In our research, we discovered a novel phase transition type.

Extraction of conjugate main-stream structures from a complex network flow.

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.