# Calculate network statistic and covariance matrix.

### Description

Calculate network statistic and covariance matrix, which is based on a multinomial distribution. Each unit (either node or edge) in the network is assumed to be sampled from a multinomial distribution based on probabilities associated with the network statistic.

### Usage

1 2 3 4 5 6 | ```
NS_Multinomial(g,
Network_stats,
mean_inflate = 0,
var_inflate = 1,
covPattern = NULL
)
``` |

### Arguments

`g` |
a network object. |

`Network_stats` |
Either 'DegreeDist' or 'DegMixing'. |

`mean_inflate` |
Add small amount to remove zero values from degree mixing matrix entries. |

`var_inflate` |
Multiply the variance by a constant. Used to avoid signular covariance matrices. |

`covPattern` |
Currently not used. |

### Value

A list of length 2 containing:

`Network Statistic` |
Network statistic of the inputted network. |

`Covariance` |
Covariance matrix for the network statistic; assumes each unit (either node or edge) is sampled from a multinomial distribution based on probabilities derived from the network statistic. |

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
g = as.network(rgraph(n=500, m=1, tprob=.01,
mode='graph', diag=FALSE,
replace=FALSE, tielist=NULL,
return.as.edgelist=FALSE),
directed = FALSE)
Prob_Distr_Params=list(NS_Multinomial(g,
Network_stats = 'DegreeDist',
mean_inflate = .05,
var_inflate = 1.05))
Prob_Distr_Params=list(NS_Multinomial(g,
Network_stats = 'DegMixing',
mean_inflate = .05,
var_inflate = 1.05))
``` |

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