基于复杂网络结构异质性的信息传输路由函数优化设计及稳定性研究

如何针对不同复杂网络结构来构建高效的路由策略是一个极具现实意义但还未引起关注的重要问题。我们前期研究发现：高效的路由策略与网络的度分布和度相关系数之间存在密切关系。由此本项目提出构建与网络结构有关的路由函数，将求解路由函数最小值所得到的路径作为路由路径的思想，以此建立一套新的路由准则理论和方法。我们首先用度分布和度相关系数作为网络结构异质性的度量，运用基于随机过程的Markov Chain 方法求解度分布和度相关系数；其次运用理论分析和仿真模拟方法对路由函数特点进行深入研究，建立路由函数与度分布之间的量化关系，对路由函数模型及参数进行优化设计，建立以网络结构为基础的新的路由准则。并以网络容量为目标，以网络结构为参变量对路由函数的稳定性和脆弱性等系列问题进行深入的理论、仿真模拟和实证研究。本项目对揭示路由策略与网络结构之间的关系具有重要意义，为异质性网络的路由策略制定奠定理论基础。

Routing strategy plays a crucial role on information transferring efficiency. Current researches focus on routing strategies on the scale-free networks and small world networks. Few consider the other kinds of network. In fact, the heterogeneity of network structure has great impact on the routing strategy. Our previous findings suggest that an effective routing strategy is closely related to the statistical characteristics of the network. Thus, this project introduces routing function concept that is associated with network structure and then explores the routing path by minimizing the proposed routing function. On condition of the previous outcomes, a new set of routing criterion and several novel approaches are developed in this project. In more detail, first of all, degree distribution and degree correlation coefficient are used to describe the heterogeneity of network structure and restructured-based Markov chain is explored to calculate the degree distribution. Secondly, characteristics of routing function are investigated through theoretical deduction as well as computer simulation in order to discover the relations between routing strategy and degree distribution and degree correlation coefficient. Based on the above results, routing function is optimized and its stability is studies. Finally, some new routing criteria are established in which taking network structure as parameter the robustness and fragility of routing function are examined by simulation experiment as well as empirical study. The purpose of this project is to explore the relationship between routing strategy and network structure, which is important to the routing strategy construction on other types of network, rather than only on scale-free and small world networks.