`redist`

provides a basic tool for assessing the (approximate) regular equivalence of actors. Two vertices \(i\) and \(j\) are said to be regularly equivalent with respect to role assignment `r`

if \(\{r(u): u\in N^+(i)\}=\{r(u): u\in N^+(j)\}\) and \(\{r(u): u\in N^-(i)\}=\{r(u): u\in N^-(j)\}\), where \(N^+\) and \(N^-\) denote out- and in-neighborhoods (respectively). RE similarity/difference scores are computed by `method`

, currently Borgatti and Everett's CATREGE algorithm (which is based on the multiplex maximal regular equivalence on \(G\) and its transpose). The “distance” between positions in this case is the inverse of the number of iterative refinements of the initial equivalence (i.e., role) structure required to allocate the positions to regularly equivalent roles (with 0 indicating positions which ultimately belong in the same role). By default, the initial equivalence structure is one in which all vertices are treated as occupying the same role; the `seed.partition`

option can be used to impose alternative constraints. From this initial structure, vertices within the same role having non-identical mixes of neighbor types are re-allocated to different roles (where “neighbor type” is initially due to the pattern of (possibly valued) in- and out-ties, cross-classified by current alter type). This procedure is then iterated until no further division of roles is necessary to satisfy the regularity condition.

Once the similarities/differences are calculated, the results can be used with a clustering routine (such as `equiv.clust`

) or an MDS (such as `cmdscale`

) to identify the underlying role structure.