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adjacency_matrix [2014/02/10 11:57]
nikolaj
adjacency_matrix [2014/02/14 13:41]
nikolaj
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 ==== 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, $\frac{1}{2}\frac{1}{3}\mathrm{tr}\,​A^3$ is the number of triangles in the graph.
 ==== Parents ==== ==== Parents ====
 === Subset of === === Subset of ===
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