Editing Adjacency matrix (section)

===Directed graphs===
The adjacency matrix of a directed graph can be asymmetric. One can define the adjacency matrix of a directed graph either such that 
# a non-zero element {{mvar|A<sub>ij</sub>}} indicates an edge from {{mvar|i}} to {{mvar|j}} or 
# it indicates an edge from {{mvar|j}} to {{mvar|i}}.

The former definition is commonly used in graph theory and social network analysis (e.g., sociology, political science, economics, psychology).<ref>
{{citation
 | title=Analyzing Social Networks
 | edition=2nd
 | first1=Steve   | last1=Borgatti
 | first2=Martin  | last2=Everett
 | first3=Jeffrey | last3=Johnson
 | publisher=SAGE
 | year=2018
 | at=p.&nbsp;20
}}</ref> The latter is more common in other applied sciences (e.g., dynamical systems, physics, network science) where {{mvar|A}} is sometimes used to describe linear dynamics on graphs.<ref>
{{citation
 | title=Networks
 | edition=2nd
 | first=Mark | last=Newman
 | publisher=Oxford University Press
 | year=2018
 | at=p.&nbsp;110
}}</ref>

Using the first definition, the [[Directed graph#Indegree and outdegree|in-degrees]] of a vertex can be computed by summing the entries of the corresponding column and the out-degree of vertex by summing the entries of the corresponding row. When using the second definition, the in-degree of a vertex is given by the corresponding row sum and the out-degree is given by the corresponding column sum.

{| class="wikitable" style="text-align: center; width: 700px;"
! Labeled graph
! Adjacency matrix
|-
| [[File:Symmetric group 4; Cayley graph 4,9; numbers.svg|250px]]
<br>[[Directed graph|Directed]] [[Cayley graph]] of [[Symmetric group|S]]<sub>4</sub>
| [[File:Symmetric group 4; Cayley graph 4,9 (adjacency matrix).svg|250px]]
<br>Coordinates are 0–23.
<br>As the graph is directed, the matrix is not necessarily [[Symmetric matrix|symmetric]].
|}