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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