双权重三角网络上的随机游走研究

Research on Random Walks on Dual-Weighted Triangular Networks

摘要: 由于确定性加权网络被广泛应用于模拟现实世界的复杂系统。本文主要研究双权重三角网络上的平均陷阱时间。我们定义内生长，即网络中已存在的内部新增节点的过程；外生长，即网络的现有结构之外添加新节点。在内生长和外生长的基础上，引入内生长权重因子q和外生长权重因子r。根据自相似网络的良好性质，通过迭代算法获得平均陷阱时间的解析式，结果显示服从指数为$\frac{ln\frac{2+4\left(q+r\right)}{2+\left(q+r\right)}}{ln5}$ 的幂律函数，该指数与内生长权重因子q和外生长权重因子r有关，且权重因子r、q越小，该陷阱捕获过程越高效。

Abstract: Deterministic weighted networks are widely used to simulate complex systems in the real world. This paper focuses on the average trapping time on dual-weighted triangular networks. We define internal growth as the process of adding new nodes within the existing structure of the network, and external growth as the process of adding new nodes outside the existing structure of the network. Based on internal and external growth, we introduce the internal growth weight factor q and the external growth weight factor r. Leveraging the excellent properties of self-similar networks, we derive the analytical formula of the average trapping time through an iterative algorithm. The results show that it follows a power-law function with an exponent of $\frac{ln\frac{2+4\left(q+r\right)}{2+\left(q+r\right)}}{ln5}$ , which is related to the internal growth weight factor q and the external growth weight factor r. Moreover, the smaller the weight factors r and q, the more efficient the trapping process.