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Graphical degree sequence validator

Can a list of vertex degrees actually be realised by a simple graph? Enter the degrees and the Erdős–Gallai / Havel–Hakimi test decides whether the sequence is graphical — a real network with those connection counts exists — and explains the verdict.

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The Graphical degree sequence validator turns Degree sequence into Graphical?, Reason, Edges (if valid), instantly and for free. For instance, with Degree sequence = 3, 3, 3, 3, 3, 3 it returns Graphical? = Yes ✓, Reason = passes Havel–Hakimi and Edges (if valid) = 9.

How to use it

  1. Enter your values: Degree sequence.
  2. Read the result instantly: Graphical?, Reason, Edges (if valid).

Frequently asked questions

What does the Graphical degree sequence validator actually compute?

It takes Degree sequence and derives Graphical?, Reason and Edges (if valid) from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

A single value: Degree sequence. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Degree sequence = 3, 3, 3, 3, 3, 3, the calculator returns Graphical? = Yes ✓, Reason = passes Havel–Hakimi and Edges (if valid) = 9. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

When would I actually use this?

Solving a triangle from what you can actually measure, converting between degrees and radians, and checking an identity before using it.

What is the most common mistake?

Leaving the calculator in the wrong angle mode. Degrees and radians differ by a factor of about 57, and the answer is wrong without ever looking wrong.

What is the difference between the Graphical degree sequence validator and the Arithmetic sequence calculator?

This one returns Graphical? and Reason; the Arithmetic sequence calculator returns nth term and Sum of terms. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Geometric sequence calculator is the closest one after this: Find the nth term and the sum of a geometric sequence.

Where do the figures come from, and how current are they?

The identities are the classical ones and the arithmetic is exact to double precision. The law-of-sines case with two sides and a non-included angle can have two valid triangles, and both are reported.

Further reading

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