对于5个顶点的子集，找到P（这些顶点之间的所有边都存在于G中）

Question

For a random graph, G, on n vertices's, each possible edge is present independently with probability k, 0 <= k <= 1.

I seek P(all edges between these vertices's are present in G)
My thoughts so far

If we have the empty subset, p = 1
If we have a one element set, p = 1
If we have a two element set, p = k
If we have a three element set, p = k^3
If we have a four element st, p = k^6
If we have a five element set, p = k^10.

If the above is correct, then I can capture the probability as the following:  P = k^(n C 2)

但是，这仅适用于二至五元素集。如果我有     一个或两个元素如果不正确则设置以下内容。如果到目前为止我正确理解了所有内容，我怎样才能捕获其他两种情况呢？

唯一可能是分段定义的函数吗？ 如果n = 0或n = 1,1 否则，k ^（n C 2）

Answer 1

实际上，您的公式适用于所有情况，因为：

n C 2 = 0, for n < 2

因此：

k^(n C 2) = k^0 = 1, for n < 2