First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models,Physical Review E

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First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-26 , DOI: 10.1103/physreve.106.034320
F Ampuero ₁ , M O Hase ₁

Affiliation

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 preestablished 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 were originally 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.

中文翻译：

时间相关 Erdős-Rényi 和 Watts-Strogatz 模型的度空间中的首次通过过程

在这项工作中，我们通过将动力学映射到度空间中的随机游走问题来研究网络中给定顶点度的时间演化。我们通过与随机游走的第一道问题平行来分析度数何时接近预先确定的值。该方法在 Erdős-Rényi 和 Watts-Strogatz 模型的时间相关版本上进行了说明，这些模型最初被制定为静态网络。我们已经成功地获得了第一次通过时间的第一和第二时刻的分析形式，并展示了它们如何依赖于网络的大小。大型网络的主要贡献

ñ

vertices 表示这些量按比例缩放

ñ / p

，在哪里

p

是链接概率。

更新日期：2022-09-26

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