eignvalues of hth distance matrix

Question

I am reading "Algebraic Graph Theory" by Biggs 1974. In the section symmetry and regularity of graphs in page 136, it is defined a set $\{A_0,A_1,...,A_d\}$ of $n\times n$ matrices as follows: $(A_h)_{rs}$ :when $d(v_r,v_s)=h$ entry $r,s$ in matrix $A_h$ is 1,otherwise it is zero. Then $A_0=I$, $A_1$ is the usual adjacency matrix $A$ of graph, and we notice that $A_0+A_1+...+A_d=J$. ($d$= diameter of graph and $J=[1]_{n\times n}$). I would like to know about eignvalue of matrix $A_h$. are there resources on the eigenvalues of this matrix? (Even for special cases) Thank you in advance.