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，这只适用于二-五元素集。如果我有一个如果不正确，一个或两个元素设置以下内容。如果到目前为止我对所有内容的理解都是正确的，那么我怎样才能捕捉到其他两种情况？

分段定义函数是唯一的可能吗？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

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）

For a subset of 5 vertices find P(all edges between these vertices are present in G)

graph-theory

probability