更改

Consider a given random graph model defined on the  probability space <math>(\Omega, \mathcal{F}, P)</math> and let <math>\mathcal{P}(G) : \Omega \rightarrow R^{m}</math> be a real valued function which assigns to each graph in <math>\Omega</math> a vector of m properties.  

Consider a given random graph model defined on the  probability space <math>(\Omega, \mathcal{F}, P)</math> and let <math>\mathcal{P}(G) : \Omega \rightarrow R^{m}</math> be a real valued function which assigns to each graph in <math>\Omega</math> a vector of m properties.  

考虑一个给定的随机图模型定义在概率空间上<math>(\Omega,\mathcal{F},P)</math> ，并且让 <math>\mathcal{P}(G):\Omega\tarrow R^{m}</math> 是一个真正的值函数，它在 <math>\Omega</math> 中为每个图赋值一个 ''m'' 属性的向量。

考虑一个给定的随机图模型定义在概率空间上<math>(\Omega,\mathcal{F},P)</math> ，并且让 <math>\mathcal{P}(G):\Omega\tarrow R^{m}</math> 是一个值是实数的函数，它在 <math>\Omega</math> 中为每个图赋值一个 ''m'' 属性的向量。

For a fixed <math>\mathbf{p} \in R^{m}</math>, ''conditional random graphs'' are models in which the probability measure <math>P</math> assigns zero probability to all graphs such that '<math>\mathcal{P}(G) \neq \mathbf{p} </math>.

For a fixed <math>\mathbf{p} \in R^{m}</math>, ''conditional random graphs'' are models in which the probability measure <math>P</math> assigns zero probability to all graphs such that '<math>\mathcal{P}(G) \neq \mathbf{p} </math>.

Special cases are conditionally uniform random graphs, where <math>P</math> assigns equal probability to all the graphs having specified properties. They can be seen as a generalization of the Erdős–Rényi model G(n,M), when the conditioning information is not necessarily the number of edges M, but whatever other arbitrary graph property <math>\mathcal{P}(G)</math>. In this case very few analytical results are available and simulation is required to obtain empirical distributions of average properties.  

Special cases are conditionally uniform random graphs, where <math>P</math> assigns equal probability to all the graphs having specified properties. They can be seen as a generalization of the Erdős–Rényi model G(n,M), when the conditioning information is not necessarily the number of edges M, but whatever other arbitrary graph property <math>\mathcal{P}(G)</math>. In this case very few analytical results are available and simulation is required to obtain empirical distributions of average properties.  

特殊情况是'''<font color="#FF8000">条件均匀随机图 Conditionally Uniform Graph </font>'''，其中 <math>p</math> 给所有具有指定性质的图赋予相等的概率。它们可以被看作是 Erdős–Rényi 模型 ''G''(''n''，''m'')的一个推广，当条件信息不一定是边的个数 ''M''，而是其他任意图性质 <math>\mathcal{P}(G)</math> 时。在这种情况下，很少有分析结果可用，需要模拟来获得平均性质的经验分布。

特殊情况是'''<font color="#FF8000">条件均匀随机图 Conditionally Uniform Graph </font>'''，其中 <math>p</math> 给所有具有指定性质的图赋予相等的概率。它们可以被看作是 Erdős–Rényi 模型 ''G''(''n''，''m'')的一个推广，当条件信息不一定是边的个数 ''M''，而是其他任意图性质 <math>\mathcal{P}(G)</math> 时。在这种情况下，很少有分析结果可用，就需要通过模拟来获得平均性质的经验分布。

==Interdependent graphs==

==Interdependent graphs==