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2-MODE>CATEGORICAL CORE/PERIPHERY
PURPOSE Uses a genetic algorithm to fit a core/periphery model to two mode data.
DESCRIPTION Simultaneously fits a core/periphery model to the data network, and identifies which actors belong in the core and which belong in the periphery and which events belong in the core and which events belong in the periphery. The rows and columns are partitioned independently. The fit is simply the correlation between the data matrix and an idealized structure matrix in which there is a one in the core block interactions and a zero in the peripheral block interactions.
PARAMETERS
Input dataset:
Name of file containing two-mode network to be analyzed. Data type: Matrix.
Row Partition: (Default = 'rowCPpart')
Name of output file which contains a cluster indicator vector for the row partition. This vector has the form (k1,k2,...ki...) where ki assigns vertex i to cluster ki and ki is either 1 or 2 where 1 is the core and 2 is the periphery, so that (1 1 2 1 2) assigns vertices 1, 2 and 4 to the core, and 3 and 5 to the periphery. This vector is not displayed at output.
Column Partition: (Default = 'colCPpart')
Name of output file which contains a cluster indicator vector for the column partition. This vector has the form (k1,k2,...ki...) where ki assigns vertex i to cluster ki and ki is either 1 or 2 where 1 is the core and 2 is the periphery, so that (1 1 2 1 2) assigns vertices 1, 2 and 4 to the core, and 3 and 5 to the periphery. This vector is not displayed at output.
LOG FILE The starting and the final correlation of the ideal structure and the permuted incidence matrix . A blocked incidence matrix dividing the actors and events independently into the core and periphery.
TIMING O(N^2) per iteration.
COMMENTS Care should be taken when using this routine.
The algorithm seeks to find the maxima of the cost function. Even if successful this result may still be a low value in which case the partition may not represent a core/periphery model.
In addition there may be a number of alternative partitions which also produce the maximum value; the algorithm does not search for additional solutions. Finally it is possible that the routine terminates at a local maxima and does not locate the desired global maxima.
To test the robustness of the solution the algorithm should be run a number of times from different starting configurations. If there is good agreement between these results then this is a sign that there is a clear split of the data into a core/periphery structure.
REFERENCES Borgatti SP and Everett M G (1999) Models of core/periphery structures. Social Networks 21 375-395
Borgatti SP and Everett M G (1997) Network analysis of 2-mode data. Social Networks 19 243-269