Description
Return n(n-1) for directed ordered pairs or half that number for unordered pairs.
A walk is an ordered sequence of visited vertices or edges, while a path normally adds structural restrictions. Sequence manipulation and endpoint checks alone do not verify that every required graph edge exists.
Return n(n-1) for directed ordered pairs or half that number for unordered pairs.
When to use this tool
Use Edge Betweenness Normalization Denominator when you need a sequence transformation, endpoint comparison, or path-related local calculation.
How to use the tool and how it works
- Enter vertices, directed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read pairs. Use the output convention below.
Require integer vertices from two through one million. Return n(n-1) for directed ordered pairs or half that number for unordered pairs.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 2; maximum 1000000. |
| directed | Directed | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| pairs | Pairs | Required. Finite number. |
{
"input": {
"vertices": 4,
"directed": false
},
"output": {
"pairs": 6
}
}Limitations and assumptions
- This is a graph-order normalization denominator, not edge betweenness itself; connectedness, reachable-pair conventions, and actual shortest paths are not 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
Validate each consecutive edge against the graph and check the required path or cycle properties. Use a dedicated traversal or shortest-path algorithm when reachability or optimality is the real question.
References
Similar or alternative tools
- Directed Graph Density Loop Policy
Use n² possible edges when allowLoops or n(n-1) otherwise, require a positive denominator and edges within it, then divide.
- Graph Distance Parity Edge Flip Tool
Compute graph distance parity edge flip from explicit bounded inputs.