A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i, d_j) on the vertex degrees d_i of a graph as [A_f(G)]_(i j) = {f(d_i, d_j) | for i, j adjacent 0 | otherwise auto right match (Das et al. 2018, Zheng et al. 2022). Special cases are summarized in the following table (c.f. Zheng et al. 2022).

ABC matrix | adjacency matrix | arithmetic-geometric matrix | randić matrix | sombor matrix