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adjacency_matrix [2014/02/14 13:41] nikolaj |
adjacency_matrix [2014/02/14 13:41] nikolaj |
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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 === | === 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. | + | 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 === |