Description Usage Arguments Details Value Author(s) References See Also Examples

Samples an undirected d-regular graph approximately uniformly at random.

1 2 3 |

`p` |
number of vertices. |

`d` |
degree of every vertex. |

`labels` |
vertex labels. |

`exclude` |
vector of vertices inducing edges that should be excluded from the sampled d-regular graph. |

`verbose` |
show progress on the calculations. |

`return.type` |
class of object to be returned by the function |

`R.code.only` |
logical; if |

This function implements the algorithm from Steger and Wormald (1999) for sampling undirected d-regular graphs from a probability distribution of all d-regular graphs on p vertices which is approximately uniform. More concretely, for all vertex degree values d that grow as a small power of p, all d-regular graphs on p vertices will have in the limit the same probability as p grows large. Steger and Wormald (1999, pg. 396) believe that for d >> sqrt(p) the resulting probability distribution will no longer be approximately uniform.

This function is provided in order to generate a random undirected graph
as input to the function `qpG2Sigma`

which samples a random
covariance matrix whose inverse (aka, precision matrix) has zeroes on those
cells corresponding to the missing edges in the input graph. d-regular
graphs are useful for working with synthetic graphical models for two
reasons: one is that d-regular graph density is a linear function of d and
the other is that the minimum connectivity degree of two disconnected vertices
is an upper bound of their outer connectivity (see Castelo and Roverato,
2006, pg. 2646).

The adjacency matrix of the resulting graph.

R. Castelo and A. Roverato

Castelo, R. and Roverato, A. A robust procedure for
Gaussian graphical model search from microarray data with p larger than n,
*J. Mach. Learn. Res.*, 7:2621-2650, 2006.

Steger, A. and Wormald, N.C. Generating random regular graphs quickly,
*Combinatorics, Probab. and Comput.*, 8:377-396.

1 2 3 4 5 | ```
set.seed(123)
A <- qpRndGraph(p=50, d=3)
summary(apply(A, 1, sum))
``` |

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