Random Labeled Tree Topology Generator

Description

Generate recursive labeled trees by attaching each later supplied ID uniformly to an earlier ID, retaining degrees and connectivity; this is not uniform over labeled trees.

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 recursive labeled trees by attaching each later supplied ID uniformly to an earlier ID, retaining degrees and connectivity; this is not uniform over labeled trees.

When to use this tool

Use this generator to create reproducible labeled tree topology 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 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, degrees, componentCount, sampling. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Keep the supplied node order and independently attach every node after the first to a uniformly selected earlier parent. Return edges, degrees, component count, and the explicit ordered-recursive-tree sampling convention.^[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 1; maximum items 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
nodes	Nodes	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; 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 0; maximum items 31.
degrees	Degrees	Required. Array of Safe integer.; minimum items 1; maximum items 32.
componentCount	Component Count	Required. Safe integer.
sampling	Sampling	Required. Text.
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"
    ],
    "seed": 42
  },
  "output": {
    "nodes": [
      "a",
      "b",
      "c",
      "d"
    ],
    "edges": [
      [
        "a",
        "b"
      ],
      [
        "a",
        "c"
      ],
      [
        "c",
        "d"
      ]
    ],
    "degrees": [
      2,
      1,
      2,
      1
    ],
    "componentCount": 1,
    "sampling": "ordered recursive tree; uniform earlier parent per node",
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

This is not uniform sampling over all labeled trees. Input ordering affects possible parents; the output is an undirected tree even though construction chooses an earlier parent.
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 Labeled Tree Topology Generator — tool.io

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