摘要翻译:
本文研究了Erdos-Renyi图中从给定的源节点到所有其他节点的最短路径的确定问题。该问题等价于确定与源节点距离相同的节点连接边的比例问题。这个量随存在边的概率的演化表现出有趣的振荡行为。为了执行我们的分析,我们引入了一种计算节点间距离分布的新方法。我们的方法优于以前的类似分析,并导致了与数值模拟非常吻合的估计。它允许我们描述当连通概率变化时出现的相变。
---
英文标题:
《Distance distribution in random graphs and application to networks
exploration》
---
作者:
Vincent D. Blondel, Jean-Loup Guillaume, Julien M. Hendrickx and
Raphael M. Jungers
---
最新提交年份:
2007
---
分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
--
一级分类:Physics 物理学
二级分类:Disordered Systems and Neural Networks 无序系统与神经网络
分类描述:Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜;随机、非周期和准周期系统的性质;无序介质中的传输;本地化;由缺陷和无序介导的现象;神经网络
--
---
英文摘要:
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior. In order to perform our analysis, we introduce a new way of computing the distribution of distances between nodes. Our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations. It allows us to characterize the phase transitions appearing when the connectivity probability varies.
---
PDF链接:
https://arxiv.org/pdf/706.3322