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Percolation is related to the robustness of the graph (called also network).  Given a random graph of <math>n</math> nodes and an average degree <math>\langle k\rangle</math>. Next we remove randomly a fraction <math>1-p</math> of nodes and leave only a fraction <math>p</math>. There exists a critical percolation threshold <math>p_c=\tfrac{1}{\langle k\rangle}</math> below which the network becomes fragmented while above <math>p_c</math> a giant connected component exists.

Percolation is related to the robustness of the graph (called also network).  Given a random graph of <math>n</math> nodes and an average degree <math>\langle k\rangle</math>. Next we remove randomly a fraction <math>1-p</math> of nodes and leave only a fraction <math>p</math>. There exists a critical percolation threshold <math>p_c=\tfrac{1}{\langle k\rangle}</math> below which the network becomes fragmented while above <math>p_c</math> a giant connected component exists.

'''<font color="#f8000">渗流 Percolation </font>''' 与图形(也称为网络)的健壮性有关。给定一个随机图形，其中的节点是 n </math > 和一个平均度 < math > > langle k rangle </math > 。接下来我们随机移除一部分节点，只留下一部分节点。存在一个临界渗透阈值，低于这个临界渗透阈值，网络变得支离破碎，而高于临界渗透阈值的网络则存在一个巨大的连接元件(图论)。

'''<font color="#FF8000">渗流 Percolation </font>''' 与图形(也称为网络)的'''<font color="#FF8000">健壮性 Robustness </font>'''有关。给定一个随机图形，其中的节点是 <math>n</math> 和一个平均度 <math>\langlek\rangle</math> 。接下来我们随机移除一部分节点，只留下一部分节点。存在一个临界渗透阈值，低于这个临界渗透阈值，网络变得支离破碎，而高于临界渗透阈值的网络则存在一个巨大的'''<font color="#FF800">连接元件 Connected Component </font>'''(图论)。

<ref>{{cite book |title= Complex Networks: Structure, Robustness and Function |authors= Reuven Cohen and [[Shlomo Havlin]] |year= 2010 |url= http://havlin.biu.ac.il/Shlomo%20Havlin%20books_com_net.php |publisher= Cambridge University Press}}</ref><ref name ="On Random Graphs" />

<ref>{{cite book |title= Complex Networks: Structure, Robustness and Function |authors= Reuven Cohen and [[Shlomo Havlin]] |year= 2010 |url= http://havlin.biu.ac.il/Shlomo%20Havlin%20books_com_net.php |publisher= Cambridge University Press}}</ref><ref name ="On Random Graphs" />

Localized percolation refers to removing a node its neighbors, next nearest neighbors etc. until a fraction of <math>1-p</math> of nodes from the network is removed. It was shown that for random graph with Poisson distribution of degrees <math>p_c=\tfrac{1}{\langle k\rangle}</math> exactly as for random removal. For other types of degree distributions <math>p_c</math> for localized attack is different from random attack

Localized percolation refers to removing a node its neighbors, next nearest neighbors etc. until a fraction of <math>1-p</math> of nodes from the network is removed. It was shown that for random graph with Poisson distribution of degrees <math>p_c=\tfrac{1}{\langle k\rangle}</math> exactly as for random removal. For other types of degree distributions <math>p_c</math> for localized attack is different from random attack

局部渗滤指的是去除一个节点的邻居、次近邻等。直到网络节点的 < math > 1-p </math > 的一部分被移除。结果表明，对于泊松分佈为 < math > p _ c = tfrac {1}{ langle k rangle } </math > 的随机图，正如对于随机删除一样。对于其他类型的度分布，局部攻击和随机攻击是不同的

'''<font color="#FF8000">局部渗滤 Localized Percolation </font>'''指的是去除一个节点的邻居、次近邻等。直到网络节点的 <math>1-p</math> 的一部分被移除。结果表明，对于泊松分布为 <math>p_c=\tfrac{1{\langle k\rangle}</math> 的随机图，正如对于随机删除一样。对于其他类型的度分布，局部攻击和随机攻击是不同的。

''(threshold functions, evolution of <math>\tilde G</math>)''

''(threshold functions, evolution of <math>\tilde G</math>)''

(threshold functions, evolution of <math>\tilde G</math>)

(threshold functions, evolution of <math>\tilde G</math>)

(阈值函数 < math > 波浪 g </math >)

('''<font color="#FF8000">阈值函数 Threshold Functions </font>'''< math > 波浪 g </math >)