atom-bond connectivity matrix

The ABC (atom-bond connectivity) matrix A_ABC of a simple graph is a weighted adjacency matrix with weight f(d_i, d_j) = sqrt((d_i + d_j - 2)/(d_i d_j)), where d_i are the vertex degrees of the graph. In other words, [A_ABC]_(i j) = {sqrt((d_i + d_j - 2)/(d_i d_j)) | for i, j adjacent 0 | otherwise auto right match .

ABC energy | ABC index | ABC spectral radius | adjacency matrix | weighted adjacency matrix