Susceptibility in Inhomogeneous Random Graphs

  • Svante Janson
  • Oliver Riordan Mathematical Institute, University of Oxford 24­29 St Giles', Oxford OX1 3LB, UK


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.

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