We study the susceptibility, i.e., the mean size of the component containing
a random vertex, in a general model of inhomogeneous random graphs. This is one
of the fundamental quantities associated to (percolation) phase transitions; in
practice one of its main uses is that it often gives a way of determining the
critical point by solving certain linear equations. Here we relate the
susceptibility of suitable random graphs to a quantity associated to the
corresponding branching process, and study both quantities in various natural
examples.Comment: 51 page