For an undirected graph, we know that nodes are adjacent to each other if there is a link that connects them. What about adjacency for directed graphs? Is it based on: 


* outgoing links: node $n$ is adjacent to node $i$ if there is a link coming out from node $n$ to node $i$
* ingoing links: node $n$ is adjacent to node $i$ if there is a link coming out from node $i$ to node $n$
* either: mixed of both above options (like adjacency in undirected graphs)


Any references would be appreciated. 



Adjacency definition for a directed graph
It depends on the author.


Some authors use the outgoing link definition, e.g. [this one](https://www.cs.cmu.edu/~adamchik/21-127/lectures/graphs_1_print.pdf): 
`In a directed graph vertex v is adjacent to u, if there is an edge leaving v and coming to u.`


Other authors use the ingoing link definition, e.g. [this one](http://faculty.cs.niu.edu/~freedman/241/241notes/241graph.htm):`insert a 1 if vertex j is adjacent to vertex i (that is, if there is an arc from vertex i to vertex j).`


There are even authors using "adjacent" as a symmetric relation, e.g. 


[this](http://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture2/lecture2.html): `We say that two vertices i and j of a directed graph are joined or adjacent if there is an edge from i to j or from j and i.` and 


[that](http://ceadserv1.nku.edu/longa//classes/mat385_resources/docs/matrix.html): 
`if a path of length 1 exists from one vertex to another (ie. the two vertices are adjacent)`.


