2. THE ADJANCENCY MATRIX and RELATED MATRICES

Adjacency matrices are square (and typical sparse) V × V or E × E symmetric matrices that reflect the adjacencies between vertices or edges in graphs (V= the number of vertices, E=number of edges). Variants of adjacency matrices, called augmented adjacency matrices [40], are adjacency matrices that posses non-zero values on main diagonal [2]. Once the adjacency matrix is known, the related graph can easily be reconstructed. The structure of the adjacency matrix depends however on the labeling of a graph, the adjacency matrix is not a graph invariant. An invariant of a graph G is a number associated with G which has the same value for any graph isomorphic to G [12].

1. The Vertex-Adjacency Matrix of Simple Graphs
2. The Linear Representation of the Vertex-Adjacency Matrix of Acyclic Structures
3. The Vertex-Adjacency Matrix of Multiple Graphs
4. The Atom-Conectivity Matrix
5. The Edge-Adjacency Matrix
6. The Vertex-Adjacency Matrix of Weighted Graphs
7. The Vertex-Adjacency Matrix of Möbius Graphs
8. The Augmented Vertex-Adjacency Matrix
9. The Edge-Weighted Edge-Adjacency Matrix
10. The Vertex-Connectivity Matrix
11. The Edge-Connectivity Matrix
12. Extended Adjacency Matrices
13. Zagreb Matrices
14. The Hückel Matrix
15. The Laplacian Matrix
16. The Generalized Laplacian Matrix
17. The Augmented Vertex-Degree Matrix

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