Random Graph Articulation Point Exercise Generator

Description

Construct candidate cut-vertex exercises and verify each vertex removal using connected-component counts, with bounded optional chords.

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.

Construct candidate cut-vertex exercises and verify each vertex removal using connected-component counts, with bounded optional chords.

When to use this tool

Use this generator to create reproducible graph articulation point exercise 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, chordCount 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, edges, candidate, beforeComponents, afterComponents, articulation, removalComponents. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Construct an ordered recursive tree and random chords, choose a node, and count components after removing each node and its incident edges. Mark the candidate an articulation point only when its removal increases the baseline component count.^[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 2; maximum items 16.
chordCount	Chord Count	Required. Safe integer; minimum 0; maximum 4.
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 2; maximum items 16.
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 1; maximum items 19.
candidate	Candidate	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
beforeComponents	Before Components	Required. Safe integer.
afterComponents	After Components	Required. Safe integer.
articulation	Articulation	Required. Boolean.
removalComponents	Removal Components	Required. Array of Safe integer.; minimum items 2; maximum items 16.
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.

json

{
  "input": {
    "nodes": [
      "a",
      "b",
      "c",
      "d"
    ],
    "chordCount": 0,
    "seed": 42
  },
  "output": {
    "nodes": [
      "a",
      "b",
      "c",
      "d"
    ],
    "edges": [
      [
        "a",
        "b"
      ],
      [
        "a",
        "c"
      ],
      [
        "c",
        "d"
      ]
    ],
    "candidate": "c",
    "beforeComponents": 1,
    "afterComponents": 2,
    "articulation": true,
    "removalComponents": [
      2,
      1,
      2,
      1
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The removed node is excluded from the remaining vertex set. A candidate need not be an articulation point, and the criterion is component increase rather than its degree or the number of removed edges.
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

Tool behavior and example: Random Graph Articulation Point Exercise Generator — tool.io

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