Description
Give each loop two degree contributions in an undirected graph or total directed degree, and one when directed and counting a single directed-degree side.
A graph's degree records how many edge incidences meet a vertex. Directed edges distinguish incoming and outgoing incidences, while loops and parallel edges require explicit counting conventions; a local degree formula does not reconstruct a graph.
Give each loop two degree contributions in an undirected graph or total directed degree, and one when directed and counting a single directed-degree side.
When to use this tool
Use Vertex Loop Degree Contribution when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter loopCount, directed, countTotalDirectedDegree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Require nonnegative integer loopCount. Give each loop two degree contributions in an undirected graph or total directed degree, and one when directed and counting a single directed-degree side.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| loopCount | Loop Count | Required. Safe integer; minimum 0. |
| directed | Directed | Required. Boolean. |
| countTotalDirectedDegree | Count Total Directed Degree | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | Contribution | Required. Safe integer. |
{
"input": {
"loopCount": 3,
"directed": false,
"countTotalDirectedDegree": false
},
"output": {
"contribution": 6
}
}Limitations and assumptions
- The flags select a convention rather than inspecting a graph; numeric output must satisfy the safe-integer contract and no adjacency or loop identity is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Build an adjacency structure and count actual incidences when a full graph is available. Validate loop, multiplicity, direction, and vertex-set assumptions before applying a simple-graph identity.
References
Similar or alternative tools
- Multigraph Loop Adjacency Diagonal Weight
Sum supplied loopWeights, double that sum on the adjacency diagonal only when doubleOnDiagonal, and always return twice the sum as degreeContribution.
- Directed Loop In Out Degree Pair
Return that count as both inDegree and outDegree and twice it as totalDegree.