Weighted Adjacency Matrix

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)]_(ij)={f(d_i,d_j)   for i,j adjacent; 0   otherwise

(Das et al. 2018, Zheng et al. 2022).

Special cases are summarized in the following table (c.f. Zheng et al. 2022).

See also

Adjacency Matrix, ABC Matrix, Arithmetic-Geometric Matrix, Randić Matrix, Sombor Matrix

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Das, K.; Gutman, I.; Milovanović, I.; Milovanović, E.; and Furtula, B. "Degree-Based Energies of Graphs." Linear Algebra Appl. 554, 185-204, 2018.Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric Matrix of Graphs and Its Applications." Appl. Math. Comput. 42, 127764, 1-11, 2023.

Cite this as:

Weisstein, Eric W. "Weighted Adjacency Matrix." From MathWorld--A Wolfram Web Resource.

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