Description
Apply bounded double-edge-swap attempts to a supplied simple undirected graph, retaining rejection reasons and verifying exact degree preservation; no uniform graph distribution is claimed.
A graph uses vertices and edges to represent relationships. Direction, duplicate handling, indexing, and traversal order affect its interpretation; returning a constructed graph together with a witness or calculated answer helps verify an algorithm.
Apply bounded double-edge-swap attempts to a supplied simple undirected graph, retaining rejection reasons and verifying exact degree preservation; no uniform graph distribution is claimed.
When to use this tool
Use this generator to create reproducible degree preserving graph rewire cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply nodes, edges, attemptCount in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read edges, initialDegrees, finalDegrees, acceptedCount, attempts. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.
Sample two distinct edges, reject shared endpoints, and propose a double-edge swap using a sampled second-edge orientation. Reject parallel-edge collisions, otherwise replace both edges and independently verify every vertex degree is unchanged.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodes | Nodes | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 4; maximum items 32. |
| edges | Edges | Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 2.; minimum items 2; maximum items 128. |
| attemptCount | Attempt Count | Required. Safe integer; minimum 1; maximum 32. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| edges | Edges | Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 2.; minimum items 2; maximum items 128. |
| initialDegrees | Initial Degrees | Required. Array of Safe integer.; minimum items 4; maximum items 32. |
| finalDegrees | Final Degrees | Required. Array of Safe integer.; minimum items 4; maximum items 32. |
| acceptedCount | Accepted Count | Required. Safe integer. |
| attempts | Attempts | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32. |
| attempts[].selected | Selected | Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 2.; minimum items 2; maximum items 2. |
| attempts[].proposed | Proposed | Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 2.; minimum items 0; maximum items 2. |
| attempts[].accepted | Accepted | Required. Boolean. |
| attempts[].reason | Reason | Required. Text. |
| randomness | Replay source and normalized 32-bit seed, or null seed for an advancing context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional safe-integer replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"nodes": [
"a",
"b",
"c",
"d"
],
"edges": [
[
"a",
"b"
],
[
"c",
"d"
]
],
"attemptCount": 1,
"seed": 42
},
"output": {
"edges": [
[
"a",
"d"
],
[
"b",
"c"
]
],
"initialDegrees": [
1,
1,
1,
1
],
"finalDegrees": [
1,
1,
1,
1
],
"acceptedCount": 1,
"attempts": [
{
"selected": [
[
"c",
"d"
],
[
"a",
"b"
]
],
"proposed": [
[
"b",
"c"
],
[
"a",
"d"
]
],
"accepted": true,
"reason": "accepted"
}
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Attempt count differs from accepted rewires, and connectivity is not preserved. A finite swap chain does not establish uniform sampling of all graphs with the same degree sequence.
- A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
Similar or alternative tools
- Random Connected Graph Test Case Generator
Generate a connected simple graph by a shuffled recursive tree plus distinct extra edges, and delegate normalization, component count and density evidence; not uniform over all connected graphs and density retains the core's 12-significant-digit convention.
- Strongly Connected Components Finder
Partition a bounded directed graph into canonical strongly connected components and return vertex memberships plus its deduplicated condensation edges using iterative Kosaraju–Sharir searches.