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**NETWORK >SUBGROUPS >F-GROUPS**

**PURPOSE **Find mutually exclusive groups based upon weak transitivity.

**DESCRIPTION **A triple of three vertices x,y and z taken from a valued graph is weakly transitive if whenever there is a tie connecting x to y and y to z stronger than some fixed value s then there exists a tie connecting x and z greater than a smaller value w.

This routine checks for weak transitivity by taking the largest value in the graph for s and a user prescribed value for w. The value of s is reduced until a triple is found that violates the weak transitivity condition. The value of s is then used to dichotomize the graph. The components (weak components for digraphs) of this dichotomized graph form the mutually exclusive F-groups.

**PARAMETERS**

** Input dataset:**

** **Name of file containing network to be analyzed. Data type: Digraph.

** **

**Cut-off value for absent ties (Default =0.0)**

** **Value below which ties are ignored. The value w in the description above.

** Output dataset(Granovetter)**

** **Name of file which will contain the strong and weak ties as described in the LOG FILE.

**Output Frequencies dataset**

** **Name of file that will contain the number and percentage of absent weak and strong ties.

**LOG FILE **Value above which ties are considered strong. That is the value s in the above description.

The F-groups with more than 2 actors in them are then displayed.

A matrix is then displayed. A value of zero indicates that a tie was below the cut-off value for absent ties ie below w. A value of 2 indicates a tie above the value of the strong tie, ie above s and ties that lie between these values are coded as 1.

A frequency table that counts the ties values in the new matrix is then presented. This gives frequencies and the frequencies expressed as a percentage.

**TIMING **O(N^3)

**COMMENTS **None

**REFERENCES **None