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NETWORK > SUBGROUPS > N-CLAN

PURPOSE Find all n-clans in a network.

DESCRIPTION An n-clan is an n-clique which has diameter less than or equal to n as an induced subgraph.  These are found by using the n-clique routine and checking the diameter condition.  

The routine will also provide an analysis of the overlapping structure of the n-clans.  This analysis gives information on the number of times each pair of actors are in the same n-clan and gives an hierarchical clustering based upon this information.

PARAMETERS
Input dataset:
Name of file containing network to be analyzed. Data type: Graph.
  
Value of N: (Default = 2)
All members of an n-clan are in an n-clique and have the additional property that they are connected by a path of length n or less in which each vertex is also a member of the n-clique.  A value of 1 would give all Luce and Perry cliques;  the maximum value of N-1 would give the components of the graph.

  

Minimum Size: (Default = 3)
This gives the smallest group size which is to be considered an n-clan. The range is 1 to N.

Analyze pattern of overlaps?  (Default = YES).
Yes means that an analysis of n-clan overlap will be performed. This includes the construction of an n-clan co-membership matrix, and an hierarchical clustering which is saved in a partition indicator matrix as described below.
No restricts the analysis to identifying n-clans only.
  
Diagram Type: (Default = 'Tree diagram')
When analyzing the overlap the clustering diagram can either be a Tree Diagram or a Dendrogram.

(Output) n-clan indicator matrix: (Default = 'NClanSets').
Name of file which contains a n-clan by actor incidence matrix.  A 1 in column i row j indicates that actor j is a member of n-clan i.  This matrix is not displayed in the LOG FILE.

(Output) Co-membership matrix: (Default = 'NClanOver').
Name of file which contains n-clan overlap matrix described in LOG FILE below.  Note that if no analysis of pattern overlaps was chosen then this file is not created.

(Output) Partition indicator matrix: (Default = 'NClanPart').
Name of file which contains partition indicator matrix derived from overlap analysis.  The partition indicator matrix corresponds to the hierarchical clustering displayed in the LOG FILE. A value of k in a column labeled i and row j means that actor j is in partition k and is in i n-clans with every other member of partition k.  Actor k is always a member of partition k, and is a representative label for the group.


LOG FILE Number of n-clans found.
List of n-clans, labeled - each n-clan is specified by the vertices it contains.

The following output is also produced if YES was inserted on the form in reply to the question 'Analyze pattern of overlaps?' The first part of the output will be the tree diagram or dendrogram corresponding to the single link clustering of the n-clan overlap matrix. In the n-clan overlap matrix  a value of k in row i column j means that vertices i and j occurred in the same n-clan k times.  The ith diagonal entry gives the number of n-clans which contain i.

The tree diagram (or a dendrogram) re-orders the actors so that they are located close to other actors in similar clusters. The level at which any pair of actors are aggregated is the point at which both can be reached by tracing from the start to the actors from right to left. The scale at the top gives the level at which they are clustered and corresponds to the number of overlaps. The diagram can be printed or saved. Parts of the diagram can be viewed by moving the mouse to the split point in a tree diagram or the beginning of a line in the dendrogram and clicking. The first click will highlight a portion of the diagram and the second click will display just the highlighted portion. To return to the original right click on the mouse. There is also a simple zoom facility simply change the values and then press enter. If the labels need to be edited (particularly the scale labels) then you should take the partition indicator matrix into the spreadsheet editor remove or reduce the labels and then submit the edited data to Tools>Dendrogram>Draw. 

   
Behind the diagram is a window containing the number of n-clans and a list as specified above. This is followed by a clustering diagram representing the same clustering as the tree diagram (or dendrogram).  The columns are rearranged and labeled.  A '' in row label i column label j means that vertex j was not in i n-clans with any other vertex.  An 'X' indicates that vertex j was in i n-clans with all vertices on the same row as j which can be found by tracing across that row without encountering a space.

 

TIMING Algorithm is exponential.

COMMENTS Usually only 2-clans or 3-clans are significant.

REFERENCES Mokken R (1979).  Cliques, clubs and clans.  Quality and Quantity 13, 161-173.