Description
Return entry zero only for a directed signed incidence convention, otherwise two.
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.
Return entry zero only for a directed signed incidence convention, otherwise two.
When to use this tool
Use Graph Self Loop Incidence Convention when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter directed, signed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read entry. Use the output convention below.
Return entry zero only for a directed signed incidence convention, otherwise two.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| directed | Directed | Required. Boolean. |
| signed | Signed | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| entry | Zero for a directed signed self-loop, two under every other supported convention. | Required. Safe integer. |
{
"input": {
"directed": true,
"signed": true
},
"output": {
"entry": 0
}
}Limitations and assumptions
- This is the tool's supplied self-loop convention, including the value two for an unsigned directed column; it does not inspect an incidence matrix or choose a universal matrix definition.
- 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.
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 Edge Source Target Incidence Sign
Return one when vertex matches target, minus one when it matches source, with cancellation for a self-loop.