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在二分法网络上随机步行
Kousuke Yakubo1, Gentaro Shimojo1, Jun Yamamoto2
1Hokkaido University, Department of Applied Physics, Sapporo 060-8628, Japan.
Physical review. E
|February 7, 2025
概括
在二分法无尺度网络 (FSFNs) 上的随机步行揭示了步行维度是恒定的,但光谱维度根据步行者的起点节点而异,突出了网络二分法效应.
科学领域:
- 复杂的网络 复杂的网络
- 网络动态 网络动态
- 碎形几何学 碎形几何学
背景情况:
- 具有无尺度和碎形属性的网络可以表现出双碎性,其中局部结构具有不同的碎形维度.
- 了解这种复杂网络上的随机步行动态对于描述它们的行为至关重要.
研究的目的:
- 在碎形无尺度网络 (FSFNs) 上调查随机步行.
- 分析双折性如何影响动态特性,特别是行走维度 (dw) 和光谱维度 (ds).
主要方法:
- 对FSFNs上的随机步行进行步行维度 (dw) 和光谱维度 (ds) 的检查.
- 分析局部碎形变化和起始节点位置如何影响这些维度.
- 对dw,ds_min和ds_max的分析表达式的导出.
主要成果:
- 步行维度 (dw) 保持不变,无论起点节点是什么.
- 光谱维度 (ds) 表现出两个值: ds_min (对于无限度的枢纽节点) 和 ds_max (对于有限度的非枢纽节点).
- ds_max等于全局光谱维度 (Ds),而这两个光谱维度源于网络的双碎性.
结论:
- 在FSFNs中的双折性导致了不同的局部光谱维度.
- 该研究为特定网络模型提供了这些发现的分析和数值确认.
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