Small-world networks: Evidence for a crossover picture

Details Small-world networks: Evidence for a crossover picture Small-world networks: Evidence for a crossover picture

1999-03-05

arxiv.org/abs/cond-mat/9903108v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 postscript figures (1 in color), Latex/Revtex/multicols/epsf. Accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.82.3180

Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the hypothesis that the appearance of small-world behavior is not a phase-transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ell$ between any two vertices of the network is a scaling function of $n / n^*$. The crossover size $n^*$ above which the network behaves as a small-world is shown to scale as $n^*(p \ll 1) \sim p^{-\tau}$ with $\tau \approx 2/3$.

Affiliated with

Also associated with

No associations

Rating

Small-world networks: Evidence for a crossover picture 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 Small-world networks: Evidence for a crossover picture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small-world networks: Evidence for a crossover picture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-179994