Random Small World Network Experiment Generator

Description

Generate bounded Watts–Strogatz-style ring rewiring experiments with retained changes and topology metrics; density inherits 12-significant-digit core rounding and connectivity is not guaranteed.

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 bounded Watts–Strogatz-style ring rewiring experiments with retained changes and topology metrics; density inherits 12-significant-digit core rounding and connectivity is not guaranteed.

When to use this tool

Use this generator to create reproducible small world network experiment 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, ringDegree, rewireProbability 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 initialEdges, edges, degrees, density, clustering, meanClustering, meanReachableDistance, reachableOrderedPairs, rewires. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Build an even-degree ring lattice and consider each initial edge for rewiring. Select a nonself, currently nonadjacent replacement target when available. Return degrees, density, local clustering, and BFS mean distance over reachable ordered pairs.^[1]

Delegated operations used for this result: density; breadth first traversal. Their calculation or parsing conventions apply to the corresponding result fields.^{[2, 3]}

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 3; maximum items 16.
ringDegree	Ring Degree	Required. Safe integer; minimum 2; maximum 14.
rewireProbability	Rewire 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
initialEdges	Initial 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 3; maximum items 120.
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 3; maximum items 120.
degrees	Degrees	Required. Array of Safe integer.; minimum items 3; maximum items 16.
density	Density	Required. Finite number.
clustering	Clustering	Required. Array of Finite number.; minimum items 3; maximum items 16.
meanClustering	Mean Clustering	Required. Finite number.
meanReachableDistance	Mean Reachable Distance	Required. Finite number. or Null.
reachableOrderedPairs	Reachable Ordered Pairs	Required. Safe integer.
rewires	Rewires	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 120.
rewires[].source	Source	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
rewires[].oldTarget	Old Target	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
rewires[].newTarget	New Target	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
rewires[].changed	Changed	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.

json

{
  "input": {
    "nodes": [
      "a",
      "b",
      "c",
      "d"
    ],
    "ringDegree": 2,
    "rewireProbability": 0,
    "seed": 42
  },
  "output": {
    "initialEdges": [
      [
        "a",
        "b"
      ],
      [
        "b",
        "c"
      ],
      [
        "c",
        "d"
      ],
      [
        "d",
        "a"
      ]
    ],
    "edges": [
      [
        "a",
        "b"
      ],
      [
        "b",
        "c"
      ],
      [
        "c",
        "d"
      ],
      [
        "d",
        "a"
      ]
    ],
    "degrees": [
      2,
      2,
      2,
      2
    ],
    "density": 0.666666666667,
    "clustering": [
      0,
      0,
      0,
      0
    ],
    "meanClustering": 0,
    "meanReachableDistance": 1.3333333333333333,
    "reachableOrderedPairs": 12,
    "rewires": [],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Rewiring can disconnect the graph and change individual degrees. The distance mean excludes unreachable pairs; it is not an all-pairs finite-distance guarantee. Node IDs must be distinct and ringDegree even and smaller than node count.
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 Small World Network Experiment Generator — tool.io
Calculation or validation: graph/density — tool.io
Calculation or validation: graph/breadth-first-traversal — tool.io

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