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-deviation 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.

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We study the large-volume asymptotics of the sum of power-weighted edge lengths e∈E |e| α in Poisson-based spatial random networks. In the regime α > d, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomena, 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 β-skeletons.