Putting the Graph Degree Sequence method to work
The sample degrees sort to (3,2,2,1), whose sum 8 equals twice the four edges.
Math calculator
Graph Degree Sequence Calculator
Compute and sort the vertex degrees of a finite simple undirected graph. Its degree sequence sits beside the working formula for a quick arithmetic check.
Graph Degree Sequence inputs
Set up the calculation
The mathematical idea behind Graph Degree Sequence
The roles assigned to vertices and undirected edges explain the operation that produces degree sequence.
Keeping a usable Graph Degree Sequence record
Count edges touching each vertex, sort, and verify the handshaking identity Σdeg=2|E|.
Assumptions to check in Graph Degree Sequence
Not every nonnegative integer sequence is graphical, and the sequence alone may not identify a unique graph.
Use Vertices as the first Graph Degree Sequence checkpoint. Confirm Undirected edges, then anticipate Degree sequence. Repeat Graph Degree Sequence without reading the prior answer. If Undirected edges differs, preserve both Graph Degree Sequence versions and both values of Degree sequence.
Tasks that depend on Graph Degree Sequence
Degree sequences summarize connectivity, identify isolated or high-degree vertices, and check graph data.
What to notice in Graph Degree Sequence
Adjacency-matrix row sums produce the same degree values. Here the requested quantity is specifically degree sequence.
A vertex degree counts incident edges; the degree sequence lists these counts from largest to smallest. Graph Degree Sequence can be compared with matrix row sums.
Applying the handshaking lemma
The degree sum must be even and must equal twice the number of distinct edges.
Auditing the Graph Degree Sequence result
Keep the Graph Degree Sequence ordering and membership rules attached to Vertices. Read Undirected edges under that same Graph Degree Sequence convention.
List a small nonempty Graph Degree Sequence example. When allowed, compare it with an empty Graph Degree Sequence case.
A practical Graph Degree Sequence check is to simplify Vertices and leave Undirected edges unchanged. The resulting Degree sequence should be easy to estimate, giving a reference point for the less convenient values in the original problem.
Questions about Graph Degree Sequence
What does Graph Degree Sequence calculate?
A vertex degree counts incident edges; the degree sequence lists these counts from largest to smallest.
When is Graph Degree Sequence useful?
Degree sequences summarize connectivity, identify isolated or high-degree vertices, and check graph data.
What can make Graph Degree Sequence misleading?
Not every nonnegative integer sequence is graphical, and the sequence alone may not identify a unique graph.
Checking Graph Degree Sequence independently
Count edges touching each vertex, sort, and verify the handshaking identity Σdeg=2|E|.