Maximum average degree

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

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