Intro to Directed Graphs | Digraph Theory

What are directed graphs, or digraphs as they are often called? We introduce digraphs and some related terms in today's graph theory lesson!

A directed graph is like a simple graph, except the edges of a digraph have - you guessed it - direction! Thus, we will see we need to use ordered pairs to describe edges of digraphs. For example, an edge going FROM the vertex u TO the vertex v is represented by the ordered pair (u, v). We say u is adjacent to v, and v is adjacent from u.

The number of edges coming out of a vertex (equivalently - the number of vertices a vertex is adjacent to) is the outdegree of the vertex. The number of edges going into a vertex (equivalently - the number of vertices a vertex is adjacent from) is the indegree of the vertex.

We call the directed edges of a digraph "arcs'. Thus, there can be two distinct arcs (u, v) and (v, u) that have the same end-vertices. Such edges are called parallel edges and DO in fact form a cycle of length 2.

How does the first theorem of graph theory work with digraphs? Think about that! Here is my lesson on the first theorem if you don't remember it:    • The First Theorem of Graph Theory | G...  

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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