Description
Generate a bounded Bernoulli graph and start node with delegated BFS and DFS answers under an explicit ascending-neighbor convention.
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 a bounded Bernoulli graph and start node with delegated BFS and DFS answers under an explicit ascending-neighbor convention.
When to use this tool
Use this generator to create reproducible graph traversal quiz 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 nodeCount, directed, edgeProbability 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 nodes, directed, edges, graph, start, convention, breadthFirst, depthFirst, unreachable. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw a directed or undirected random graph, choose a start node, and delegate breadth-first and depth-first traversal using ascending ASCII neighbor labels. Return both answers and nodes unreachable from that start.1
Delegated operations used for this result: breadth first traversal; depth first traversal. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodeCount | Node Count | Required. Safe integer; minimum 2; maximum 12. |
| directed | Directed | Required. Boolean. |
| edgeProbability | Edge 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 |
|---|---|---|
| nodes | Nodes | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 12. |
| directed | Directed | Required. Boolean. |
| edges | Edges | Required. Array of Array of Safe integer; minimum 0; maximum 11.; minimum items 2; maximum items 2.; minimum items 0; maximum items 144. |
| graph | Graph | Required. Object. |
| start | Start | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64. |
| convention | Convention | Required. Text. |
| breadthFirst | Breadth First | Required. Object; no unknown keys. |
| breadthFirst.visitOrder | Visit Order | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 12. |
| breadthFirst.depths | Depths | Required. Object. |
| depthFirst | Depth First | Required. Object; no unknown keys. |
| depthFirst.visitOrder | Visit Order | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 12. |
| depthFirst.depths | Depths | Required. Object. |
| unreachable | Unreachable | Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 0; maximum items 12. |
| 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": {
"nodeCount": 4,
"directed": false,
"edgeProbability": 0.7,
"seed": 42
},
"output": {
"nodes": [
"n00",
"n01",
"n02",
"n03"
],
"directed": false,
"edges": [
[
0,
1
],
[
0,
2
],
[
1,
2
],
[
1,
3
],
[
2,
3
]
],
"graph": {
"n00": [
"n01",
"n02"
],
"n01": [
"n00",
"n02",
"n03"
],
"n02": [
"n00",
"n01",
"n03"
],
"n03": [
"n01",
"n02"
]
},
"start": "n01",
"convention": "Ascending ASCII neighbor labels; BFS discovery order and DFS preorder. Only this convention is graded; other neighbor orders may also be valid traversals.",
"breadthFirst": {
"depths": {
"n01": 0,
"n00": 1,
"n02": 1,
"n03": 1
},
"visitOrder": [
"n01",
"n00",
"n02",
"n03"
]
},
"depthFirst": {
"depths": {
"n01": 0,
"n00": 1,
"n02": 2,
"n03": 3
},
"visitOrder": [
"n01",
"n00",
"n02",
"n03"
]
},
"unreachable": [],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The answer key grades BFS discovery order and DFS preorder under this neighbor convention; other neighbor orders can also be valid traversals. The graph need not be connected.
- 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.