I am currently working on a graph problem regarding DNA sequencing and created a graph which contains all binary words of length k which have some certain properties and have a directed edge inbetween if the first word's last k-1 letters and the second word's first k-1 letters are the same. If I now have a look at the adjacency matrix I get a structure that looks oddly familiar, but I can't put a finger on it. This is how the adjacency matrix looks like (black entries are zero, white ones are one):
My first observation is that the matrix is point symmetric in regard to the center of the matrix and secondly the lines almost look like some kind of band matrix, but only in approximate form. I searched the web for different symmetry classes but couldn't find a matrix class describing point symmetric matrices. Did you ever see such a structure or do you know to which kind of classes this matrix could belong?