  Many multivariate data sets exhibit a form of positive dependence, which can
either appear globally between all variables or only locally within particular
subgroups. A popular notion of positive dependence that allows for localized
positivity is positive association. In this work we introduce the notion of
extremal positive association for multivariate extremes from threshold
exceedances. Via a sufficient condition for extremal association, we show that
extremal association generalizes extremal tree models. For H\"usler--Reiss
distributions the sufficient condition permits a parametric description that we
call the metric property. As the parameter of a H\"usler--Reiss distribution is
a Euclidean distance matrix, the metric property relates to research in
electrical network theory and Euclidean geometry. We show that the metric
property can be localized with respect to a graph and study surrogate
likelihood inference. This gives rise to a two-step estimation procedure for
locally metrical H\"usler--Reiss graphical models. The second step allows for a
simple dual problem, which is implemented via a gradient descent algorithm.
Finally, we demonstrate our results on simulated and real data.
