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arXiv · 1110.1134

Dynamics of Random Graphs with Bounded Degrees

E. Ben-Naim·P. L. Krapivsky
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Abstract

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.

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BibTeXRIS

E. Ben-Naim, P. L. Krapivsky. 2011-11-15. Dynamics of Random Graphs with Bounded Degrees. https://doi.org/10.1088/1742-5468%2F2011%2F11%2Fp11008

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