  Spatial random graphs capture several important properties of real-world
networks. We prove quenched results for the continuum space version of
scale-free percolation introduced in [DW18]. This is an undirected
inhomogeneous random graph whose vertices are given by a Poisson point process
in $\mathbb R^d$. Each vertex is equipped with a random weight and the
probability that two vertices are connected by an edge depends on their weights
and on their distance. Under suitable conditions on the parameters of the
model, we show that, for almost all realizations of the point process, the
degree distributions of all the nodes of the graph follow a power law with the
same tail at infinity. We also show that the averaged clustering coefficient of
the graph is self-averaging. In particular, it is almost surely equal to the
the annealed clustering coefficient of one point, which is a strictly positive
quantity.
