Bootstrap percolation on complex networks.
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: f, the fraction of vertices initially activated, and p, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any f>0 and p>0, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.
Baxter
G J
GJ
Departamento de Física, I3N, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal. gjbaxter@ua.pt
Dorogovtsev
S N
SN
Goltsev
A V
AV
Mendes
J F F
JF
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*