Matrix power

Once the connectivity matrix for the first level de Bruijn diagram has been set up, it can be raised to powers; each time option t is used, the power is increased by 1. At the same time, the power matrix is displayed in the matrix panel; from there it can be analyzed, even copied by a screen dump if it is so desired.

By exhibiting a visual image of the matrix, some of the details of the linkages can be seen, such as their number and density. The matrix is not sorted, so all but the most obvious block diagonal or block triangular forms tend to be obscured until the higher powers.

The matrix display distinguishes only non-zero elements, but the element and the trace are always shown just above the header line; 0 is always the number of the zero partial neighborhood.

Two matrices are maintained by the program. One is the first level connection matrix, displayed by typing m. The other is a work matrix; it contains the powers generated by option t, and can be displayed by typing n.

When the work matrix is used to hold the second level diagram, the labelling arrangement is different; the matrix uses a coded form of the link as the link's matrix element, -1 for a non-link. The matrix can be viewed using option o instead of n.

Conversion to standard form can be effected by option ~, but then no more samples can be generated without starting all over again. On the other hand, t and option 8 could then be used to gather statistics on the second level diagram.

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Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx