Abstract: Define the scale-free Gilbert graph based on a Boolean model
with heavy-tailed radius distribution on the d-dimensional torus by
connecting two centers by an edge if at least one of the balls contains
the center of the other. We investigate two asymptotic properties of
this graph as the size of the torus tends to infinity:
i) the tail index associated with the asymptotic distribution of the sum
of all power-weighted incoming and outgoing edge lengths at a randomly
chosen vertex.
ii) chemical distances between distant nodes.