I've started with a somewhat irregular six-sided figure. Note that points A and C are connected. Also, note that A and F are not connected. To make an adjacency matrix , one merely makes a grid of ones and zeros. Ones indicate a connection, or an adjacency.
Zeroes indicate no connection.
You can copy the matrix in the third box, and paste it into the Matrix calculator . Then indicate you want the characteristic polynomial. I've noticed that the characteristic polynomials of symmetric figures are more factorable than asymmetric figures. I don't know, I'm just asking. Highly symmetric graphs give highly factorable polynomials.