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**DATA > RANDOM > MULTINOMIAL**

**PURPOSE** Generate random valued graphs in which the values are distributed by user assigned probabilities.

**DESCRIPTION** The user specifies N, the total number of cases in the simulated "sample". The algorithm randomly distributes the N cases into the cells of the adjacency matrix. This distribution can either be uniform, in which case each cell has the same probability of being assigned one of the cases, or the distribution can be user specified. In this case the algorithm randomly assigns each case in proportion to the cell probabilities. The probabilities can be specified by row, column or individual cells. The result is a value for each directed arc in the network.

**PARAMETERS**

** Number of nodes** (Default = 10)

Number of nodes in each valued adjacency matrix to be created.

**Number of graphs** (Default = 1)

Number of random matrices to be created.

**Total number of cases (sum of values)**

Total number of values to be distributed across all cells in adjacency matrix. Default is n(n-1) where n is the number of nodes.

** What probabilities will you supply** (Default = Matrix)

Choices are:

M**atrix** - a single probability is used for the entire matrix.

**Row **- a set of probabilities, one for each row is used.

** Column**** **- a set of probabilities, one for each column is used.

**Row*Column** - two sets of probabilities are prescribed, one for the rows and one for the columns. The probability for each cell is the product of the probabilities prescribed for its row and column.

**Cell** - a complete matrix of probabilities, one for each cell is prescribed.

Once an option has been selected the routine highlights parameters which are dependent on the option selected.

**Row option**

** Row probabilities dataset:**

Name of file which contains probabilities for each row, it is assumed that the required probabilities will be contained in a matrix.

**Probabilities are Row or Column of this dataset: **(Default = Column)

Specify Row or Column as required.

**Which Row/Column** (Default = 1)

Number of row or column required.

** Column option**

** ****Column probabilities dataset:**

Name of file which contains probabilities for each column, it is assumed that the required probabilities will be contained in a matrix.

**Probabilities are Row or Column of this dataset:** (Default = Column)

Specify Row or Column as required.

**Which Row/Column:** (Default = 1)

Number of row or column required.

** Row*Column option**

Two datasets are provided row probabilities as in row option and column probabilities as in column option.

**Cell option**

** **

** ****Cell probabilities dataset:**

Name of file which contains matrix of probabilities.

** Generate self loops:** (Default = No)

If NO then there will be no ties on the diagonal.

**Random number seed:**

UCINET generates a different random number as a default each time it is run. Use of the same seed will result in the same 'random' graph. The range is 1 to 32000.

** Output dataset** (Default = 'MultinomialRandomGraph')

Name of file which will contain generated random network.

**LOG FILE** The log file contains a display of each random matrix.

**TIMING **O(N^2).

**COMMENTS** None.

**REFERENCES** None.