Description
Use n² possible edges when allowLoops or n(n-1) otherwise, require a positive denominator and edges within it, then divide.
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.
Use n² possible edges when allowLoops or n(n-1) otherwise, require a positive denominator and edges within it, then divide.
When to use this tool
Use Directed Graph Density Loop Policy when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter vertices, edges, allowLoops. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read possibleEdges, density. Use the output convention below.
Require vertices 1-1000000 and nonnegative integer edges. Use n² possible edges when allowLoops or n(n-1) otherwise, require a positive denominator and edges within it, then divide.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 1; maximum 1000000. |
| edges | Edges | Required. Safe integer; minimum 0. |
| allowLoops | Allow Loops | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| possibleEdges | Possible Edges | Required. Finite number. |
| density | Density | Required. Finite number. |
{
"input": {
"vertices": 3,
"edges": 3,
"allowLoops": false
},
"output": {
"possibleEdges": 6,
"density": 0.5
}
}Limitations and assumptions
- A singleton without loops is rejected because density is undefined under this contract; supplied counts assume at most one edge per ordered pair and no adjacency is checked.
- 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
- Directed Loop In Out Degree Pair
Return that count as both inDegree and outDegree and twice it as totalDegree.
- Graph Self Loop Incidence Convention
Return entry zero only for a directed signed incidence convention, otherwise two.