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adjacency_matrix [2014/02/13 16:13] 127.0.0.1 external edit |
adjacency_matrix [2014/03/21 11:11] (current) |
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| ===== Adjacency matrix ===== | ===== Adjacency matrix ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $n\in\mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $n\in\mathbb N$ | |
| - | | @#FFBB00: $ A \in \mathrm{it}(n) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ A \in \mathrm{it}(n) $ | |
| - | | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb N) $ | | + | | @#55EE55: postulate | @#55EE55: $ A \in \mathrm{SquareMatrix}(n,\mathbb N) $ | |
| ==== Discussion ==== | ==== 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. | 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, $\frac{1}{2}\cdot\frac{1}{3}\cdot\mathrm{tr}\,A^3$ is the number of triangles in the graph. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
