NETWORK > CORE/PERIPHERY > CATEGORICAL
PURPOSE Uses a genetic algorithm to fit a core/periphery model to the 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.
Name of file containing network to be analyzed. Data type: Valued Digraph.
Data are Pos or Neg: (Default = POSITIVE)
Use positive to indicate that larger values imply a stronger relationship. Use negative to indicate that larger values in the data imply a more distant relationship.
Algorithm: (Default = CORR)
The fit function is the correlation between the permuted data matrix and an ideal structure matrix consisting of ones in the core block interactions and zeros in the peripheral block interactions. This value is maximized.
The fit function is the density of the core block interactions.This value is maximized.
The fit function is the element wise product of the permuted data matrix and an ideal structure matrix consisting of ones in the core block interactions and zeros in the peripheral block interactions.This value is maximized.
The fit function is the number of entries in the peripheral block interactions. This value is minimized.
Density of core-to-periphery blocks:
This sets the density of the core to periphery ties in the ideal structure matrix.. If left blank or the word missing is entered these ties are ignored. Any other value is entered into every cell in the off diagonal blocks of the ideal structure matrix.
Maximum # of iterations: (Default = 200)
Sets the maximum number of iterations performed.
Population Size: (Default = 100)
Number of genes in the population.
Output partition: (Default = 'CLUSPART')
Name of output file which contains a cluster indicator vector. This vector has the form (k1,k2,...ki...) where ki assigns vertex i to cluster ki where 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.
Output cluster indicator matrix: (Default = 'CLUSTERS')
Name of file which contains a cluster by actor incidence matrix. A 1 in row i column j indicates that actor j is a member of cluster i, i = 1 or 2 with 1 representing the core and 2 the periphery. This matrix is not displayed in the LOG FILE.
The starting and the final correlation of the ideal structure and the permuted adjacency matrix (regardless of which option was chosen). A listing of the members of the core and the periphery. A blocked adjacency matrix dividing the actors into the core and periphery.
TIMING O(N^2) per iteration. Correlation is considerably slower than the other options
COMMENTS Care should be taken when using this routine.
The algorithm seeks to find the minima (maxima) of the cost function. Even if successful this result may still be a high (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 minimum (maximum) value; the algorithm does not search for additional solutions. Finally it is possible that the routine terminates at a local minima (maxima) and does not locate the desired global minima (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