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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) Both sides previous revision Previous revision 2014/02/14 13:41 nikolaj 2014/02/14 13:41 nikolaj 2014/02/13 16:13 external edit2014/02/10 11:57 nikolaj 2014/02/10 11:56 nikolaj 2014/02/08 02:59 nikolaj 2014/02/08 02:12 nikolaj 2014/02/08 02:11 nikolaj old revision restored (2013/12/21 19:57) Next revision Previous revision 2014/02/14 13:41 nikolaj 2014/02/14 13:41 nikolaj 2014/02/13 16:13 external edit2014/02/10 11:57 nikolaj 2014/02/10 11:56 nikolaj 2014/02/08 02:59 nikolaj 2014/02/08 02:12 nikolaj 2014/02/08 02:11 nikolaj old revision restored (2013/12/21 19:57) Line 1: Line 1: ===== 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 ===