  We study the large-volume asymptotics of the sum of power-weighted edge
lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In
the regime $\alpha > d$, we provide a set of sufficient conditions under which
the upper large deviations asymptotics are characterized by a condensation
phenomenon, meaning that the excess is caused by a negligible portion of
Poisson points. Moreover, the rate function can be expressed through a concrete
optimization problem. This framework encompasses in particular directed,
bidirected and undirected variants of the $k$-nearest neighbor graph, as well
as suitable $\beta$-skeletons.
