摘要翻译:
我从回顾随机图的一些基本性质开始。然后,我考虑了随机游动在复杂网络中的作用,并展示了如何使用它们来解释为什么在实际数据集中发现如此多的长尾分布。其关键思想是,在许多情况下,这一过程涉及到网络中近邻属性的复制,这是一种短随机游动,进而产生一种自然的优先附着机制。将此应用于固定规模的网络,我证明复制和创新是具有特殊数学性质的过程,包括对任意参数值和任意时间精确求解简单模型的能力。最后,我看了一下这个基本模型的变体。
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英文标题:
《Randomness and Complexity in Networks》
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作者:
T.S.Evans
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最新提交年份:
2007
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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
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英文摘要:
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key idea is that in many cases the process involves copying of properties of near neighbours in the network and this is a type of short random walk which in turn produce a natural preferential attachment mechanism. Applying this to networks of fixed size I show that copying and innovation are processes with special mathematical properties which include the ability to solve a simple model exactly for any parameter values and at any time. I finish by looking at variations of this basic model.
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PDF链接:
https://arxiv.org/pdf/711.0603