Admittedly, this is less of a research-y question (and admittedly, a little non-algorithmic trivial question), but I am hoping to get some meaningful answer.Given an undirected graph $G = (V, E)$, with $n = |V|$ vertices and $m = |E|$ edges, what is a good upper bound on $\sum_{v \in V} \deg^2(v)$ in terms of $m$ and $n$.Two obvious upper bounds are $O(n^3)$ and $O(m^2)$, which are quite weak for extremely sparse and extremely dense graphs respectively. Is there any reference to find a non-trivial (asymptotic) bound? For example, can we bound it as $O(m^\alpha n^\beta)$ for some $\alpha < 2$ and $\beta < 3$? 
Bounds on sum of squares of node degrees in undirected graphs
graph theory;co.combinatorics