加速网络的主方程分析
Master-equation analysis of accelerating networks
摘要：
在许多现实世界的网络中，节点和链路添加的速率是时间相关的。这一观察激发了加速网络的定义。对加速网络的研究相对较少，以前分析其度分布的努力都采用了平均场技术。相比之下，我们表明，这是可能的，应用主方程的方法，这样的网络发展。我们提供了完整的时间依赖表达式的度分布的规范情况下的随机和优先连接在网络进行恒定加速的演变。这些结果与模拟结果非常吻合。我们注意到，一个不断增长的，非平衡网络经历恒定的加速度与随机附件是等效的经典随机图，弥合非平衡和经典平衡网络之间的差距。
英文摘要：
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing, non-equilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between non-equilibrium and classical equilibrium networks.
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