The matching function between vertices i and j is based upon the following. For each k in i's neighborhood search for an m in j's neighborhood of similar value. A measure of similar values is based upon the absolute difference of magnitudes of ties. This measure is then weighted by the degree of equivalence between k and m at the previous iteration. It is this match that is optimized. This is summed for all members of i's neighborhood over all relations and normalized to provide the current iteration's measure of equivalence between i and j. The procedure is repeated for all pairs of vertices for a fixed number of iterations.

The result of this iterative procedure is a symmetric similarity matrix which provides a measure of regular equivalence. This matrix is automatically submitted to a single link hierarchical clustering routine.

Undirected data will give a trivial result with all non-isolate vertices being equivalent.

Number of iterations to be performed. Larger values increase the differentiation between vertices. A value of 3 has often been used and is now customary.

YES performs the analysis on the valued distance matrix. If symmetric data is to be analyzed then this option will provide a non-trivial analysis of the data.

The clustering diagram can either be a

Name of file which contains REGE measure of regular equivalence described in LOG FILE.

Name of file which contains a partition indicator matrix corresponding to the single link hierarchical clustering displayed in the LOG FILE. A value of k in a row labeled i and column j means that vertex j is in partition k at level i. Vertex k is always a member of partition k and is a representative label for the group. This matrix is not displayed in the LOG FILE.

Behind the dendrogram is an alternative cluster diagram. The columns have been rearranged and labeled. A '·' in row labeled i column label j indicates that vertex j is in a singleton cluster at level i. An 'X' indicates that vertex j is in a non-trivial cluster at level i, all other members of j's cluster are found by tracing along the row labeled i in both directions from column j until a space is encountered in each direction. The column labels corresponding to an 'X' which are connected to j's X are all members of j's cluster at level i.

An actor by actor REGE similarity matrix. Values vary between 0 and 100. A value of 100 indicates strict regular equivalence.

For these reasons users with binary or nominal data are advised to use CATEGORICAL REGE

White D R and Reitz K P (1983). Graph and semi-group homomorphisms on networks of relations. Social Networks 6, 193-235.