REGGE.FOR Is the implementation of 1983 "Graph and Semigroup Homomorphisms" (drw & K.P.Reitz) Social Networks 5:193-234.

Regge is now implemented in the original version in NetMiner (you should open a new copy of the brower because you cannot get back here from Netminer

The purpose of regular equivalence analysis is to find structural positions that relate in equivalent
ways to other such positions.

See input-output analysis for a new example

There are now (2004) two matching implementations of Regdi and Regge for the PC

RegDis.for as used in Smith and White (1992)

RegSim.for as in White and Reitz (1983), with normalization

The executables can be downloaded at

RegDis.exe as used in Smith and White

The original CRAY routines were not changed, but both these versions have an improved normalization routine to equalize row and column totals. The procedure uses 20 iterations of taking row and column sums and dividing each entry by the square root of its row and its column sum. For distance the zero in the diagonal does not affect normalization, but regular equivalence diagonals have to be set temporarily to zero for the normalization to work, and then finally reset to the highest value in the matrix when finished. Row and column totals will equal .5 in all cases, plus the highest value in the equivalence matrix. Hence all marginals are equalized and they do not enter into the pattern of results. In SVD analysis, the first factor will always have constant loadings, so it is only factors 2 and 3 (and possibly others) that account for variance.

It is because values in the matrix will be low that the similarity routine sets the diagonals equal to the largest entry. For both the distance and similarity methods, the most appropriate analysis (using UCInet) is probably SVD, looking at factors 2 and higher. If the ratio of the second to third SVD factor is more than 10:1 in variance accounted for, a "pure" single factor model may be assumed. If there is more than a 3:1 ratio the single factor model is still dominant.

The input data format is simply to have two header lines as shown and then a series of single headers followed by comma-separated entries for each row of the matrix, in this case 33 lines each with 33 entries.

4 matrices

33 nodes

1977 year

3201,0,20861,3,269,33,1,14,0,1,1,0,0,0,1,0,0,0,6,0,0,0,0,0,0,352,11,134,3,0,2,4,2
23,19,25,1,0,0,6,1,341,0,169,3,1,0,1,0,0,0,1,0,0,0,0,0,0,65,0,4,0,0,0,0,0

Etc

This file goes on to include four matrices. Strip the headers and substitute blanks for commas to import any one matrix to UCInet as a raw data file. Preliminary tests show the similarity and distants methods tend to give similar results.

Output files are named REGDNORMtitle and REGSNORMtitle for the Distance and Similarity programs, respectively, where ‘title’ is the first four digits of the last title line in the input data.

Also in 2004, Woodrow Denham and I tried to solve some of the problems of equivalence analysis of section and subsection-based marriage structure in Australia, having complete genealogical data and the reference terminology network for the Alyawarra. For the genealogical/marriage network alone, RegSim.for was unable to identify clusters beyond section structure, which is the highest-level role model (everyone does marry correctly by section). Two variants were tried.

This new class of algorithms were called **motif equivalences** because they impose additional rules or
constraints that make up a motif or pattern that shapes the equivalence relations

1. Color-Eq.for, Color-Eq.exe.
This has an additional constraint such that any primary genealogical link (marriage, parent/child, but not sibling)
nullifies the possibility of equivalence. What is created is the condition for a graph homomorphism or
*coloring*, where lines connect sets, and no line can occur within equivalence sets.

2. MotifClu.for, MotifClu.exe. In addition to the above constraint, this variant reads a file containing partition numbers assigned to nodes and imposes a low equivalence (set by the user, e.g., 0.01) for all pairs of nodes that belong to different partitions. (If this were set to zero, positive equivalence values could occur only within each partition group.)