Description
Preserve the count for a within-component edge or subtract one for a connecting edge.
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.
Preserve the count for a within-component edge or subtract one for a connecting edge.
When to use this tool
Use Graph Component Merge Count Step 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 components, endpointsSameComponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read components, delta. Use the output convention below.
Require positive integer components and at least two when endpointsSameComponent is false. Preserve the count for a within-component edge or subtract one for a connecting edge.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| components | Components | Required. Safe integer; minimum 1. |
| endpointsSameComponent | Endpoints Same Component | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| components | Components | Required. Safe integer. |
| delta | Delta | Required. Safe integer. |
{
"input": {
"components": 5,
"endpointsSameComponent": false
},
"output": {
"components": 4,
"delta": -1
}
}Limitations and assumptions
- Component membership is supplied and no graph is inspected or changed; this does not independently compute connected components.
- 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 Contraction Selfloop Count Delta
Add edgesBetween to loop count only when keepContractedEdges, otherwise preserve existingLoops.