更改

The theory of random graphs studies typical properties of random graphs, those that hold with high probability for graphs drawn from a particular distribution.  For example, we might ask for a given value of <math>n</math> and <math>p</math> what the probability is that <math>G(n,p)</math> is connected.  In studying such questions, researchers often concentrate on the asymptotic behavior of random graphs&mdash;the values that various probabilities converge to as <math>n</math> grows very large. Percolation theory characterizes the connectedness of random graphs, especially infinitely large ones.

The theory of random graphs studies typical properties of random graphs, those that hold with high probability for graphs drawn from a particular distribution.  For example, we might ask for a given value of <math>n</math> and <math>p</math> what the probability is that <math>G(n,p)</math> is connected.  In studying such questions, researchers often concentrate on the asymptotic behavior of random graphs&mdash;the values that various probabilities converge to as <math>n</math> grows very large. Percolation theory characterizes the connectedness of random graphs, especially infinitely large ones.

随机图理论研究随机图的典型性质，即从特定分布中抽取的图的高概率性质。例如，我们可以要求一个给定的值 < math >n</math > 和 < math >p</math > 什么是 < math >G(n，p)</math > 连接的概率。在研究这些问题时，研究人员往往集中在随机图的渐近行为上——各种概率收敛到的值变得非常大。<font color="##f8000">渗流理论 Percolation Theory </font>刻画了随机图，特别是无穷大图的连通性。

随机图理论研究随机图的典型性质，即从特定分布中抽取的图的高概率性质。例如，我们可以要求一个给定的值 < math >n</math > 和 < math >p</math > 什么是 < math >G(n，p)</math > 连接的概率。在研究这些问题时，研究人员往往集中在随机图的渐近行为上——各种概率收敛到的值变得非常大。'''<font color="#FF8000">渗流理论 Percolation Theory </font>'''刻画了随机图，特别是无穷大图的连通性。

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.

Percolation 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="#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)。

<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" />