Graph Degree Sequence Calculator

Work out graph degree sequence instantly with clear inputs, formula shown and shareable results.

About Graph Degree Sequence Calculator

The handshaking lemma says the degrees sum to twice the number of edges, so an odd total is impossible. Euler's condition then decides traversability: all degrees even gives a closed circuit, exactly two odd gives an open path.

Formulas

Handshaking lemma

Σ deg(v) = 2·|E|

Eulerian condition

circuit ⇔ every degree even; path ⇔ exactly two odd degrees

Worked example

With the default values below, Graph Degree Sequence Calculator returns Number of edges of 6.0. Change any input above and every figure here is recalculated in your browser.

Inputs used

Degree of each vertex: 3, 3, 2, 2, 2
Assume the graph is simpleone of Yes, simple graph, No, multigraph allowed: Yes, simple graph

Results

Number of edges: 6.0
Sum of degrees: 12
Realisability: Sequence is consistent with a graph
Eulerian condition: Eulerian path exists but not a circuit (exactly two odd degrees)

Step by step

1Values used
2Handshaking lemma
3Eulerian condition
4Number of edges= 6.0
5Sum of degrees= 12
6Realisability= Sequence is consistent with a graph
7Eulerian condition= Eulerian path exists but not a circuit (exactly two odd degrees)

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 1 decimal place, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For degrees 3, 3, 2, 2, 2?

The sum is 12, so there are 6 edges, and with two odd degrees an Eulerian path exists but no circuit.

Why must the degree sum be even?

Every edge contributes 1 to each of its two endpoints, so the total is always exactly twice the edge count.