Dynamics of Random Graphs with Bounded Degrees

Details Dynamics of Random Graphs with Bounded Degrees Dynamics of Random Graphs with Bounded Degrees

2011-10-06

arxiv.org/abs/1110.1134v2

J. Stat. Mech. P11008 (2011)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures, 2 tables

Scientific paper

10.1088/1742-5468/2011/11/P11008

We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this linking step until a regular random graph, where all nodes have degree d, forms. We view this process as a multivariate aggregation process, and formally solve the evolution equations using the Hamilton-Jacoby formalism. We calculate the nontrivial percolation thresholds for the emergence of the giant component when d>=3. Also, we estimate the number of steps until the giant component spans the entire system and the total number of steps until the regular random graph forms. These quantities are non self-averaging, namely, they fluctuate from realization to realization even in the thermodynamic limit.

Affiliated with

Also associated with

No associations

Rating

Dynamics of Random Graphs with Bounded Degrees 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 Dynamics of Random Graphs with Bounded Degrees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of Random Graphs with Bounded Degrees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-180760