  The object of study is a soft random geometric graph with vertices given by a
Poisson point process on a line and edges between vertices present with
probability that has a polynomial decay in the distance between them. Various
aspects of such models related to connectivity structures have been studied
extensively. In this paper we study the random graph from the perspective of
extreme value theory and focus on the occurrence of single long edges. The
model we investigate has non-periodic boundary and is parameterized by a
positive constant $\alpha$, which is the power for the polynomial decay of the
probabilities determining the presence of an edge. As a main result we provide
a precise description of the magnitude of the longest edge in terms of
asymptotic behavior in distribution. Thereby we illustrate a crucial dependence
on the power $\alpha$ and we recover a phase transition which coincides with
exactly the same phases in [2].
