# Maximum boundary size of the resulting qp-graphs

### Description

Calculates and plots the size of the largest vertex boundary as function of the non-rejection rate.

### Usage

1 2 3 |

### Arguments

`nrrMatrix` |
matrix of non-rejection rates. |

`n` |
number of observations from where the non-rejection rates were estimated. |

`threshold.lim` |
range of threshold values on the non-rejection rate. |

`breaks` |
either a number of threshold bins or a vector of threshold breakpoints. |

`vertexSubset` |
subset of vertices for which their maximum boundary size is calculated with respect to all other vertices. |

`plot` |
logical; if TRUE makes a plot of the result; if FALSE it does not. |

`qpBoundaryOutput` |
output from a previous call to |

`density.digits` |
number of digits in the reported graph densities. |

`logscale.bdsize` |
logical; if TRUE then the scale for the maximum boundary size is logarithmic which is useful when working with more than 1000 variables; FALSE otherwise (default). |

`titlebd` |
main title to be shown in the plot. |

`verbose` |
show progress on calculations. |

### Details

The maximum boundary is calculated as the largest degree among all vertices of a given qp-graph.

### Value

A list with the maximum boundary size and graph density as function of threshold, the threshold on the non-rejection rate that provides a maximum boundary size strictly smaller than the sample size n and the resulting maximum boundary size.

### Author(s)

R. Castelo and A. Roverato

### References

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.

### See Also

`qpHTF`

`qpGraphDensity`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
require(mvtnorm)
nVar <- 50 ## number of variables
maxCon <- 5 ## maximum connectivity per variable
nObs <- 30 ## number of observations to simulate
set.seed(123)
A <- qpRndGraph(p=nVar, d=maxCon)
Sigma <- qpG2Sigma(A, rho=0.5)
X <- rmvnorm(nObs, sigma=as.matrix(Sigma))
## the higher the q the less complex the qp-graph
nrr.estimates <- qpNrr(X, q=1, verbose=FALSE)
qpBoundary(nrr.estimates, plot=FALSE)
nrr.estimates <- qpNrr(X, q=5, verbose=FALSE)
qpBoundary(nrr.estimates, plot=FALSE)
``` |

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