I have been playing around with the concept of an adjacency matrix and its corresponding graph.
For those who don’t know, a graph is a set of connected, points, sort of a diagram.
An adjacency matrix is a set of boolean (1 or 0) values where the ith column, jth row is the true value of “point i is connected to point j”. So, if you have two points, if the first point is connected to the second, and there is no loop from the first point to itself and no loop from the second point to itself the matrix will look like this:
| 0 1 |
| 1 0 |
Anyway, I started think about what graph you get when you multiply the adjacency matrix by itself. Turns out you can interpret it as a “weighted graph” (with any non-zero value interpreted as true, and the number assigned, the “weight” given the edge. Turns out I am seeing interesting cycles. More on this later.