Class RandomRegularGraphGenerator<V,​E>

  • Type Parameters:
    V - graph node type
    E - graph edge type
    All Implemented Interfaces:

    public class RandomRegularGraphGenerator<V,​E>
    extends Object
    implements GraphGenerator<V,​E,​V>
    Generate a random $d$-regular undirected graph with $n$ vertices. A regular graph is a graph where each vertex has the same degree, i.e. the same number of neighbors.

    The algorithm for the simple case, proposed in [SW99] and extending the one for the non-simple case [W99], runs in expected $\mathcal{O}(nd^2)$ time. It has been proved in [KV03] to sample from the space of random d-regular graphs in a way which is asymptotically uniform at random when $d = \mathcal{O}(n^{1/3 - \epsilon})$.

    [KV03] Kim, Jeong Han, and Van H. Vu. "Generating random regular graphs." Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. ACM, 2003. [SW99] Steger, Angelika, and Nicholas C. Wormald. "Generating random regular graphs quickly." Combinatorics, Probability and Computing 8.4 (1999): 377-396. [W99] Wormald, Nicholas C. "Models of random regular graphs." London Mathematical Society Lecture Note Series (1999): 239-298.

    Emilio Cruciani