Description
Add edgesBetween to loop count only when keepContractedEdges, otherwise preserve existingLoops.
Connected components partition a graph by reachability. Removing bridges creates an edge-connectivity partition; this differs from vertex-biconnected decomposition, which concerns articulation vertices and has different blocks.
Add edgesBetween to loop count only when keepContractedEdges, otherwise preserve existingLoops.
When to use this tool
Use Edge Contraction Selfloop Count Delta when you need a component or bridge-related count under the specified undirected graph model.
How to use the tool and how it works
- Enter edgesBetween, existingLoops, keepContractedEdges. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read loops, delta. Use the output convention below.
Require positive integer edgesBetween and nonnegative existingLoops. Add edgesBetween to loop count only when keepContractedEdges, otherwise preserve existingLoops.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| edgesBetween | Edges Between | Required. Safe integer; minimum 1. |
| existingLoops | Existing Loops | Required. Safe integer; minimum 0. |
| keepContractedEdges | Keep Contracted Edges | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| loops | Loops | Required. Safe integer. |
| delta | Delta | Required. Safe integer. |
{
"input": {
"edgesBetween": 3,
"existingLoops": 2,
"keepContractedEdges": true
},
"output": {
"loops": 5,
"delta": 3
}
}Limitations and assumptions
- This is a supplied contraction convention; the selected vertices, actual edge multiplicity, other loop creation, graph simplification, and mutation are not evaluated.
- 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
Traverse the supplied graph for an independently derived partition. Use articulation-point and vertex-biconnected algorithms when vertex removal, rather than edge removal, is the relevant failure model.
References
Similar or alternative tools
- Edge Biconnected Component Count
Traverse the undirected edge-indexed adjacency to identify bridges using discovery and low-link values, then count vertex components reachable without bridge edges.
- Edge Subdivision Vertex Edge Delta
Add the inserted count to both vertices and edges and return it as edgeDelta.