标题： 固定规模网络中的非线性优先重连作为扩散过程 显示英文标题

标题： Nonlinear preferential rewiring in fixed-size networks as a diffusion process

摘要： 我们提出一个动态网络模型，其中节点和边的总数保持不变，但边根据非线性优先分离和重新连接不断重新布线。 假设幂律核的指数为 alpha 和 beta，度分布演化的稳态表现出二级相变——在 alpha = beta 时从相对均匀变为高度不均匀（出现星型结构）。 在此临界区域内分布的时间演化被证明遵循非线性扩散方程，最终得到指数为 -alpha 和 1-alpha 的纯幂律或混合幂律。 显示英文摘要

摘要： We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta, the stationary states the degree distributions evolve towards exhibit a second order phase transition - from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha = beta. Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power-laws, of exponents -alpha and 1-alpha.