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