  In this paper, we study the connectivity of a one-dimensional soft random
geometric graph (RGG). The graph is generated by placing points at random on a
bounded line segment and connecting pairs of points with a probability that
depends on the distance between them. We derive bounds on the probability that
the graph is fully connected by analysing key modes of disconnection. In
particular, analytic expressions are given for the mean and variance of the
number of isolated nodes, and a sharp threshold established for their
occurrence. Bounds are also derived for uncrossed gaps, and it is shown
analytically that uncrossed gaps have negligible probability in the scaling at
which isolated nodes appear. This is in stark contrast to the hard RGG in which
uncrossed gaps are the most important factor when considering network
connectivity.
