Adjacency matrices are yet another way of generating siteswaps and transitions between them. In June 2002, I wrote a program for generating juggling adjacency matrices. I sent the source code for my program to Colin Wright, who had introduced me to the mathematics behind juggling at a lecture that he gave. Very kindly, Colin demonstrated better programming practices, which made the program much more easily extendable. This would have been very hard to learn without a mentor. Now the program can generate adjacency matrices which only use certain heights of throws. I added this feature following the observation that there are many different 5 ball siteswaps, which only use the throws 9,1 & 5, for example, 915, 91, 9151. Because you can’t do the transition from 5 to 91, for example, using these 3 permitted throws, you often get self-contained matrices woven together in the big adjacency matrix, so the program separates the big matrix into its constituents, and deletes states that can’t be reached and can’t be left.

The following adjacency matrices are available for download in PDF format:

- 3 Object Adjacency Matrix
- 4 Object Adjacency Matrix
- 5 Object Adjacency Matrix
- 5 Object Adjacency Matrix, throws 9, 5 & 1
- Multi-Object Adjacency Matrix

More will follow soon… (just tell me what you want)

In addition the program used to generate the adjacency matrices is available, if your needs are not met above: