Editing Adjacency matrix (section)

===Undirected graphs===
The convention followed here (for undirected graphs) is that each edge adds 1 to the appropriate cell in the matrix, and each loop (an edge from a vertex to itself) adds 2 to the appropriate cell on the diagonal in the matrix.<ref>{{cite conference |url=https://books.google.com/books?id=wp7XsCAm_9EC&pg=PA63 |title=Expander graphs and codes |last1=Shum |first1=Kenneth |last2=Blake |first2=Ian |date=2003-12-18 |publisher=American Mathematical Society |book-title=Volume 68 of DIMACS series in discrete mathematics and theoretical computer science |pages=63 |isbn=9780821871102 |conference=Algebraic Coding Theory and Information Theory: DIMACS Workshop, Algebraic Coding Theory and Information Theory }}</ref> This allows the degree of a vertex to be easily found by taking the sum of the values in either its respective row or column in the adjacency matrix.

{|class="wikitable" style="text-align: center; width: 700px;"
![[Labeled graph]]
!Adjacency matrix
|-
|[[Image:6n-graph2.svg|200px]]
|<!-- The first cell is a 2, not a 1, because of the self-loop. Otherwise, its degree would not match its row or column sum. --><math>\begin{pmatrix}
2 & 1 & 0 & 0 & 1 & 0\\
1 & 0 & 1 & 0 & 1 & 0\\
0 & 1 & 0 & 1 & 0 & 0\\
0 & 0 & 1 & 0 & 1 & 1\\
1 & 1 & 0 & 1 & 0 & 0\\
0 & 0 & 0 & 1 & 0 & 0
\end{pmatrix}</math>
<br>Coordinates are 1–6.
|-
|[[File:Symmetric group 4; Cayley graph 1,5,21 (Nauru Petersen); numbers.svg|250px]]
<br>[[Nauru graph]]
|[[File:Symmetric group 4; Cayley graph 1,5,21 (adjacency matrix).svg|250px]]
<br>Coordinates are 0–23.
<br>White fields are zeros, colored fields are ones.
|}