  We study large deviations of the size of the largest connected component in a
general class of inhomogeneous random graphs with iid weights, parametrized so
that the degree distribution is regularly varying. We derive a large-deviation
principle with logarithmic speed: the rare event that the largest component
contains linearly more vertices than expected is caused by the presence of
constantly many vertices with linear degree. Conditionally on this rare event,
we prove distributional limits of the weight distribution and component-size
distribution.
