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adjacency_matrix [2014/02/14 13:41] nikolaj |
adjacency_matrix [2014/03/21 11:11] |
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| - | ===== Adjacency matrix ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $n\in\mathbb N$ | | ||
| - | | @#FFBB00: $ A \in \mathrm{it}(n) $ | | ||
| - | |||
| - | | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb N) $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | If the indices $i,j$ label two vertices of a [[finite undirected graph]], then the value $A_{ij}$ determines the number of edges joining them. | ||
| - | === Theorems === | ||
| - | The number $(A^n)_{ij}$ is the number of paths from $v_i$ to $v_j$. And so, for example, $\frac{1}{2}\frac{1}{3}\mathrm{tr}\,A^3$ is the number of triangles in the graph. | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Hermitian matrix]] | ||
| - | === Related === | ||
| - | [[Finite undirected graph]] | ||
