Anomalous percolating properties of growing networks

Details Anomalous percolating properties of growing networks Anomalous percolating properties of growing networks

2001-06-07

arxiv.org/abs/cond-mat/0106141v2

Phys. Rev. E 64, 066110 (2001)

Physics

Condensed Matter

Statistical Mechanics

12 pages revtex, 3 figures

Scientific paper

10.1103/PhysRevE.64.066110

We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and the distribution of vertices among connected components. We show that all the derivatives of the giant connected component size $S$ over the rate $b$ of the emergence of new edges are zero at the percolation threshold $b_c$, and $S \propto \exp\{-d(\gamma)(b-b_c)^{-1/2}\}$, where the coefficient $d$ is a function of the degree distribution exponent $\gamma$. In the entire phase without the giant component, these networks are in a ``critical state'': the probability ${\cal P}(k)$ that a vertex belongs to a connected component of a size $k$ is of a power-law form. At the phase transition point, ${\cal P}(k) \sim 1/(k\ln k)^2$. In the phase with the giant component, ${\cal P}(k)$ has an exponential cutoff at $k_c \propto 1/S$. In the simplest particular case, we present exact results for growing exponential networks.

Affiliated with

Also associated with

No associations

Rating

Anomalous percolating properties of growing networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Anomalous percolating properties of growing networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anomalous percolating properties of growing networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-419059