Susceptibility in inhomogeneous random graphs

Svante Janson, Oliver Riordan

Published 2009-05-04Version 1

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.