Maximum average degree

Let G=(V,E) be an undirected graph. For a node set $$X \subseteq V$$ , $$i_G(X)$$ denotes the number of induced edges in X. The maximum average degree of G is

$$\mbox{mad}(G)= 2\max_{\emptyset \neq X \subseteq V} \frac{ i_G(X)}{|X|}.$$