  We introduce a notion of intrinsically H\"older graphs in metric spaces.
Following a recent paper of Le Donne and the author, we prove some relevant
results as the Ascoli-Arzel\`a compactness Theorem, Ahlfors-David regularity
and the Extension Theorem for this class of sections. In the first part of this
note, thanks to Cheeger theory, we define suitable sets in order to obtain a
vector space over $\R$ or $\C,$ a convex set and an equivalence relation for
intrinsically H\"older graphs. These last three properties are new also in the
Lipschitz case. Throughout the paper, we use basic mathematical tools.
