The Sombor matrix A_Sombor of a simple graph is a weighted adjacency matrix with weight f(d_i, d_j) = sqrt(d_i^2 + d_j^2), where d_i are the vertex degrees of the graph. In other words, [A_Sombor]_(i j) = {sqrt(d_i^2 + d_j^2) | for i, j adjacent 0 | otherwise auto right match . Its largest eigenvalue is called the Sombor spectral radius, half the sum of its matrix elements is the Sombor index, and the sum of absolute values of its eigenvalues is the Sombor energy.

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