复杂运输网络分析的马尔可夫链方法
Markov Chain Methods For Analyzing Complex Transport Networks
摘要：
我们已经开发了一个复杂的运输网络的稳态理论，用于模拟商品，信息，病毒，意见或交通的流动。我们的方法是基于使用的马尔可夫链定义的图形表示的运输网络，允许有效的网络设计，网络性能评估，嵌入，分区和网络容错分析。随机游动将图嵌入到欧氏空间中，在欧氏空间中距离和角度获得了明确的统计解释。随机游动定义在运输网络的对偶图表示上，描述了非随机商品流在素图上的均衡构型。该理论将许多网络概念统一到一个框架中，并且还可以优雅地扩展到描述由有向图和多个交互网络表示的网络。
英文摘要：
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph representations of transport networks allowing for the effective network design, network performance evaluation, embedding, partitioning, and network fault tolerance analysis. Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation. Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs. This theory unifies many network concepts into one framework and can also be elegantly extended to describe networks represented by directed graphs and multiple interacting networks.
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