What is the degree of a vertex?

In an undirected graph, the degree of a vertex is the number of edges incident to it. Self-loops (an edge from a vertex to itself) count twice by convention.

What is the handshaking lemma?

The handshaking lemma states that the sum of all vertex degrees equals twice the number of edges. This tool displays that sum so you can verify it instantly.

How does a directed graph differ?

In a directed graph each edge has a source and a destination. The tool reports in-degree (edges arriving) and out-degree (edges leaving) separately for every vertex.

What edge formats are accepted?

Each line should contain two vertex labels separated by a space, comma, or hyphen — for example "A B", "A,B", or "A-B". Vertex labels can be numbers or letters.

Are self-loops supported?

Yes. A self-loop "A A" contributes 2 to vertex A's degree in an undirected graph, and 1 each to its in-degree and out-degree in a directed graph.

Graph Degree Calculator

Name: Graph Degree Calculator
Availability: InStock
Author: Nham Vu

Enter an edge list and instantly see each vertex's degree, the total degree sum, and the sorted degree sequence.

Edge List Input

Edges (one per line, e.g. A B)

Graph type

Undirected Directed

Examples

Enter an edge list and click Calculate to see results.

Vertex Degrees

Degree Sequence

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Summary

Enter an edge list and instantly see each vertex's degree, the total degree sum, and the sorted degree sequence.

How it works

Enter edges one per line in the format "A B" or "A-B" (e.g. "1 2" means an edge between vertex 1 and vertex 2).
Choose whether the graph is undirected or directed.
Click Calculate to process the edge list.
Each vertex's degree (or in-degree/out-degree for directed) appears in the results table.
The degree sequence and total degree sum are shown below the table.

Use cases

Verify the handshaking lemma: total degree always equals twice the number of edges.
Identify hub vertices (high-degree nodes) in network analysis.
Compute in-degree and out-degree distributions for directed graphs.
Check whether a degree sequence is graphical (can represent a valid graph).
Study graph properties for algorithms courses and homework.
Quickly validate adjacency data before building a graph data structure.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu