论文标题
时间依赖于时间依赖的Erdős-rényi和watts-strogatz模型的第一学期过程
First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models
论文作者
论文摘要
在这项工作中，我们通过将动力学映射到学位空间中的随机行走问题中，研究了网络中给定顶点程度的时间演变。我们分析该度通过与随机步行的第一步问题平行的近似预先建立的值近似。该方法在Erdős-rényi和Watts-Strogatz模型的时间相关版本上进行了说明，该版本最初是作为静态网络配制的。我们已经成功地为第一个通用时间的第一矩和第二瞬间获得了分析形式，并显示了它们如何依赖网络的大小。 $ n $顶点的大型网络的主要贡献表明，这些数量的比例$ n/p $，其中$ p $是链接概率。
In this work, we investigate the temporal evolution of the degree of a given vertex in a network by mapping the dynamics into a random walk problem in degree space. We analyze when the degree approximates a pre-established value through a parallel with the first-passage problem of random walks. The method is illustrated on the time-dependent versions of the Erdős-Rényi and Watts-Strogatz models, which originally were formulated as static networks. We have succeeded in obtaining an analytic form for the first and the second moments of the first-passage time and showing how they depend on the size of the network. The dominant contribution for large networks with $N$ vertices indicates that these quantities scale on the ratio $N/p$, where $p$ is the linking probability.
