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In mathematics, random graph is the general term to refer to probability distributions over graphs.  Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph.

In mathematics, random graph is the general term to refer to probability distributions over graphs.  Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph.

在数学中，'''<font color="#ff8000">随机图 Random Graph </font>'''是指图上的概率分布的一般术语。随机图可以简单地用概率分布表示，也可以用生成它们的随机过程表示。随机图的理论位于图论和概率论的交叉点上。从数学的角度来看，随机图被用来回答有关典型图的性质的问题。它的实际应用在所有需要对复杂网络进行建模的领域都能找到——许多随机图模型就此被人们所熟知，它反映了在不同领域遇到的不同类型的复杂网络。在数学上，随机图几乎完全指的是 Erdős-Rényi 随机图模型。在其他情况下，任何图形模型都可以称为随机图。

在数学中，'''<font color="#ff8000">随机图 Random Graph </font>'''是指图上的概率分布的一般术语。随机图可以简单地用概率分布表示，也可以用生成它们的随机过程表示。随机图的理论位于图论和概率论的交叉点上。从数学的角度来看，随机图被用来回答有关典型图的性质的问题。它的实际应用在所有需要对复杂网络进行建模的领域都能找到——许多随机图模型就此被人们所熟知，它反映了在不同领域遇到的不同类型的复杂网络。在数学上，随机图几乎完全指的是 '''<font color="#FF8000">Erdős-Rényi 随机图模型 Erdős–Rényi Random Graph Model </font>'''。在其他情况下，任何图形模型都可以称为随机图。

A closely related model, the Erdős–Rényi model denoted G(n,M), assigns equal probability to all graphs with exactly M edges. With 0 ≤ M ≤ N, G(n,M) has <math>\tbinom{N}{M}</math> elements and every element occurs with probability <math>1/\tbinom{N}{M}</math>.  The latter model can be viewed as a snapshot at a particular time (M) of the random graph process <math>\tilde{G}_n</math>, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly from the set of missing edges.

A closely related model, the Erdős–Rényi model denoted G(n,M), assigns equal probability to all graphs with exactly M edges. With 0 ≤ M ≤ N, G(n,M) has <math>\tbinom{N}{M}</math> elements and every element occurs with probability <math>1/\tbinom{N}{M}</math>.  The latter model can be viewed as a snapshot at a particular time (M) of the random graph process <math>\tilde{G}_n</math>, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly from the set of missing edges.

一个密切相关的模型，'''<font color="#FF8000">Erdős-Rényi 模型 Erdős–Rényi Model </font>'''表示''G'' (''n'',''M'')，给每一个正好有''M''条边的图赋予等概率。当0≤ ''M'' ≤ ''N'' 时，''G'' (''n'',''M'')具有 <math>\tbinom{N}{M}</math> 元素，且每个元素都以概率<math>1/\tbinom{N}{M}</math> 出现。后一个模型可以看作是随机图过程<math>\tilde{G}_n</math>某个特定时间(''M'')的一个快照，这个时间(''M'')是从 n 个顶点开始没有边的一个随机过程，每个步骤均匀地从缺失的边集中选择一个新的边。

一个密切相关的模型，Erdős-Rényi模型表示''G'' (''n'',''M'')，给每一个正好有''M''条边的图赋予等概率。当0≤ ''M'' ≤ ''N'' 时，''G'' (''n'',''M'')具有 <math>\tbinom{N}{M}</math> 元素，且每个元素都以概率<math>1/\tbinom{N}{M}</math> 出现。后一个模型可以看作是随机图过程<math>\tilde{G}_n</math>某个特定时间(''M'')的一个快照，这个时间(''M'')是从 n 个顶点开始没有边的一个随机过程，每个步骤均匀地从缺失的边集中选择一个新的边。