An n-Hadamard graph is a graph on 4n vertices defined in terms of a Hadamard matrix H_n = (h)_(i j) as follows. Define 4n symbols r_i^+, r_i^-, c_i^+, and c_i^-, where r stands for "row" and c stands for "columns, " and take these as the vertices of the graph. Then construct two edges (r_i^±, c_j^±) for each matrix element such that h_(i j) = 1 and (r_i^±, c_j^∓) for each matrix element such that h_(i j) = - 1 .

distance-regular graph | Hadamard design | Hadamard matrix