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NETWORK > ROLES  & POSITIONS> EXACT > MAXSIM 

PURPOSE Calculate a measure of approximate exact equivalence for valued data.  

The measure is the Euclidean distance of independently sorted profiles.  Binary data is automatically converted to a distance matrix before analysis.

DESCRIPTION A coloring of a graph G is exact if whenever two vertices u and v of G are colored the same they have the same color neighborhoods with exactly the same number of each color. 

The sorted profile of vertex i of a valued network is the row vector of i with the elements placed in ascending order.  The maxsim distance is the Euclidean distance between the sorted profile of a pair of vertices.  For directed data the column profiles are automatically concatenated on to the row profiles.  

Binary data is automatically converted to a reciprocal distance matrix so that the i,jth entry contains the reciprocal of the distance between i and j.

PARAMETERS
Input dataset:
Name of file containing network to be analyzed. Data type: Valued graph. Binary data is automatically converted to a reciprocal distance matrix.

Treat diagonal values as valid?  (Default = NO).
If NO diagonals are ignored.

Diagram Type: (Default = 'Dendrogram')
The clustering diagram can either be a Tree Diagram or a Dendrogram.

Output dataset: (Default = 'MaxSim').
Name of file which will contain maxsim distance matrix.


LOG FILE Single link hierarchical clustering dendrogram (or tree diagram) of the maxsim distance matrix. 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 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 plot is the actor by actor maxsim matrix. This is followed by an alternative clustering diagram representing the same information as above.  The columns are rearranged and labeled.  A '·' in column label j at level x means that actor j is not in any cluster at level x.  An x indicates that actor j is in a cluster at this level together with those actors which can be traced across that row without encountering a space.

TIMING O(N^3).

COMMENTS This algorithm is not suitable for data in which the values have low variance or are sparse.

The algorithm (by Borgatti and Everett) is an adaptation of an algorithm due to Everett and Borgatti (1988).

REFERENCES Everett M G (1985).  'Role similarity and complexity in social networks'.  Social Networks 7, 353-359.

Everett M G and Borgatti S P (1988).  'Calculating role similarities: An algorithm that helps determine the orbits of a graph'.  Social Networks 10, 71-91.