A similar concentration result is available for subgaussian random variables. It is known as the Hanson-Wright inequality and is given in Proposition 2 below. First versions of this inequality can be found in Hanson and Wright [5] and Wright [9], although with a weaker statement than Proposition 2 below since these results involve ||| (|aij |) |||2 instead of |||A|||2. Recent proofs of this con...

We present a short way of proving the inequalities obtained by Wright in [Journal of Graph Theory, 4: 393 – 407 (1980)] concerning the number of connected graphs with l edges more than vertices. 1. Preliminaries For n ≥ 0 and −1 ≤ l ≤ ( n 2 ) − n, let c(n, n + l) be the number of connected graphs with n vertices and n+ l edges. Quantifying c(n, n+ l) represents one of the fundamental tasks in t...