Description
Generate graphs with optional duplicate listings and delegate edge normalization and matrix round trips, comparing semantic edges independently of listing order.
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.
Generate graphs with optional duplicate listings and delegate edge normalization and matrix round trips, comparing semantic edges independently of listing order.
When to use this tool
Use this generator to create reproducible graph representation round trip corpus 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 count, nodeCount, directed, allowSelfLoops, edgeProbability, duplicateProbability 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 cases. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw raw adjacency entries with optional duplicate edges and self-loops. Normalize semantic edges, convert to a matrix and back, and require the reconstructed normalized nodes and edges to match.1
Delegated operations used for this result: normalize edge list; adjacency list to matrix. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 16. |
| nodeCount | Node Count | Required. Safe integer; minimum 1; maximum 12. |
| directed | Directed | Required. Boolean. |
| allowSelfLoops | Allow Self Loops | Required. Boolean. |
| edgeProbability | Edge Probability | Required. Finite number; minimum 0; maximum 1. |
| duplicateProbability | Duplicate Probability | Required. Finite number; minimum 0; maximum 1. |
| 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 |
|---|---|---|
| cases | Cases | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16. |
| cases[].directed | Directed | Required. Boolean. |
| cases[].nodes | Nodes | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 12. |
| cases[].rawAdjacency | Raw Adjacency | Required. Object. |
| cases[].normalizedEdges | Normalized 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 0; maximum items 144. |
| cases[].matrix | Matrix | Required. Array of Array of Safe integer; minimum 0; maximum 1.; minimum items 1; maximum items 12.; minimum items 1; maximum items 12. |
| cases[].reconstructedAdjacency | Reconstructed Adjacency | Required. Object. |
| cases[].reconstructedEdges | Reconstructed 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 0; maximum items 144. |
| cases[].semanticallyEquivalent | Semantically Equivalent | Required. Boolean. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric 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": {
"count": 1,
"nodeCount": 3,
"directed": false,
"allowSelfLoops": false,
"edgeProbability": 0.7,
"duplicateProbability": 0.5,
"seed": 42
},
"output": {
"cases": [
{
"directed": false,
"nodes": [
"n00",
"n01",
"n02"
],
"rawAdjacency": {
"n00": [
"n01",
"n01"
],
"n01": [
"n02",
"n02"
],
"n02": []
},
"normalizedEdges": [
[
"n00",
"n01"
],
[
"n01",
"n02"
]
],
"matrix": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
],
"reconstructedAdjacency": {
"n00": [
"n01"
],
"n01": [
"n00",
"n02"
],
"n02": [
"n01"
]
},
"reconstructedEdges": [
[
"n00",
"n01"
],
[
"n01",
"n02"
]
],
"semanticallyEquivalent": true
}
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Semantic round-trip equality does not preserve duplicate multiplicity, raw neighbor order, or arbitrary weights. directed controls whether an edge's orientation is significant.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- 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 Graph Articulation Point Exercise Generator
Construct candidate cut-vertex exercises and verify each vertex removal using connected-component counts, with bounded optional chords.
- Random Graph Bridge Cut Exercise Generator
Construct a recursive connected graph with optional chords and label candidate/all-edge removals by delegated component changes.