===== Adjacency matrix =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $n\in\mathbb N$ | 

| @#FFBB00: definiendum | @#FFBB00: $ A \in \mathrm{it}(n) $ |

| @#55EE55: postulate   | @#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, $\frac{1}{2}\cdot\frac{1}{3}\cdot\mathrm{tr}\,A^3$ is the number of triangles in the graph.
==== Parents ====
=== Subset of ===
[[Hermitian matrix]]
=== Related ===
[[Finite undirected graph]]