Diameter bound for a fixed-density binomial random graph
= Diameter bound for a fixed-density binomial random graph
{title2=$\Pr(\operatorname{diam}G(n,p)\leq2)\to1$}
For fixed $0<p<1$, the <missing common-neighbour count in a binomial random graph> has <expectation> tending to zero. The <Markov inequality> therefore shows that every pair has a <common neighbour> with probability tending to one. On that event every <graph distance> is at most two, so the <graph> is <connected> and its <graph diameter> is at most two.