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It turns out that if the vertex set is countable then there is, up to isomorphism, only a single graph with this property, namely the Rado graph. Thus any countably infinite random graph is almost surely the Rado graph, which for this reason is sometimes called simply the random graph. However, the analogous result is not true for uncountable graphs, of which there are many (nonisomorphic) graphs satisfying the above property.

It turns out that if the vertex set is countable then there is, up to isomorphism, only a single graph with this property, namely the Rado graph. Thus any countably infinite random graph is almost surely the Rado graph, which for this reason is sometimes called simply the random graph. However, the analogous result is not true for uncountable graphs, of which there are many (nonisomorphic) graphs satisfying the above property.

结果表明，如果顶点集是可数的，那么在同构意义下，只有一个图具有这个性质，即 Rado 图。因此，任何可数无限随机图几乎可以肯定是 Rado 图，由于这个原因，有时被简称为随机图。然而，对于不可数图类似的结果是不正确的，不可数图中有许多(不同构)图满足上述性质。

结果表明，如果顶点集是可数的，那么在同构意义下，只有一个图具有这个性质，即 Rado 图。因此，任何可数无限随机图几乎可以肯定是 Rado 图，由于这个原因，有时被简称为随机图。然而，对于'''<font color="#FF8000">不可数图 Uncountable Graph </font>'''类似的结果是不正确的，不可数图中有许多'''<font color="#F8000">(不同构)图 Nonisomorphic Graph </font>'''满足上述性质。

Another model, which generalizes Gilbert's random graph model, is the random dot-product model. A random dot-product graph associates with each vertex a real vector.  The probability of an edge uv between any vertices u and v is some function of the dot product u • v of their respective vectors.

Another model, which generalizes Gilbert's random graph model, is the random dot-product model. A random dot-product graph associates with each vertex a real vector.  The probability of an edge uv between any vertices u and v is some function of the dot product u • v of their respective vectors.

另一个模型，概括了吉尔伯特的随机图模型，是随机点积模型。一个随机点积图将每个顶点与一个实向量相关联。任意顶点 ''u'' 和 ''v'' 之间的边 ''uv'' 的概率是它们各自向量的点积 ''u'' · ''v'' 的某个函数。

另一个模型，概括了吉尔伯特的随机图模型，是'''<font color="#FF8000">随机点积模型 Random Dot-product Model</font>'''。一个随机点积图将每个顶点与一个实向量相关联。任意顶点 ''u'' 和 ''v'' 之间的边 ''uv'' 的概率是它们各自向量的点积 ''u'' · ''v'' 的某个函数。