In-Degree and Out-Degree in Directed Graphs: Understanding Vertex Degrees
Learn about in-degree and out-degree in directed graphs. This guide explains how to calculate the in-degree and out-degree of vertices, provides examples, and clarifies the difference between directed and undirected graph vertex degrees.
In-Degree and Out-Degree in Directed Graphs
Degree of a Vertex in an Undirected Graph
In an undirected graph (where edges don't have a direction), the degree of a vertex is simply the number of edges connected to it. It's denoted as deg(v), where 'v' is the vertex.
For a complete graph with 'n' vertices, the degree of each vertex is n-1 (because each vertex is connected to every other vertex except itself).
Examples: Degree in Undirected Graphs
(Illustrative undirected graphs should be included here, with the degree of each vertex clearly labeled.)
In-Degree and Out-Degree in Directed Graphs
In a directed graph (where edges have a direction), each vertex has two types of degrees:
- In-degree (deg-(v)): The number of edges pointing into vertex v.
- Out-degree (deg+(v)): The number of edges pointing out of vertex v.
The total degree of a vertex in a directed graph is the sum of its in-degree and out-degree: deg(v) = deg-(v) + deg+(v).
Examples: In-Degree, Out-Degree, and Total Degree in Directed Graphs
(Illustrative directed graphs should be included here, with the in-degree, out-degree, and total degree of each vertex clearly labeled. Several examples are provided in the original text.)
Conclusion
The concepts of in-degree, out-degree, and total degree are crucial for understanding and analyzing directed graphs, providing a way to quantify the flow of information or relationships in a network.