Six-Degrees Hop Small-World Estimator
Conditional log(N)/log(k) tree-like branching estimate under caller effective degree, not shortest-path census, six-degree law or actual small-world guarantee.
Description
A tree-like small-world approximation relates population size to effective branching degree.
A tree-like small-world approximation relates population size to effective branching degree.1
It produces a conditional hop estimate rather than shortest paths from a measured social network.
When to use Six-Degrees Hop Small-World Estimator
Use this tool to obtain conditionalTreeLikeHopEstimate from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
How to use Six-Degrees Hop Small-World Estimator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter callerEffectiveReachableDegree, callerPopulationSize, using the field meanings and rules below, then run the tool.
- Read result.conditionalTreeLikeHopEstimate. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerEffectiveReachableDegree | Caller effective reachable degree | number | Required |
| callerPopulationSize | Caller population size | number | Required |
Require an effective branching degree greater than one and a positive population size. Return natural log(population) divided by natural log(degree); no integer population or hop rounding is enforced. Population below one can return a negative estimate. No observed graph or shortest-path search is used.
conditionalHops=ln(populationSize)/ln(effectiveDegree) Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or qualified reference | object |
| result.conditionalTreeLikeHopEstimate | Conditional Tree Like Hop Estimate | number |
{
"input": {
"callerEffectiveReachableDegree": 2,
"callerPopulationSize": 64
},
"output": {
"result": {
"conditionalTreeLikeHopEstimate": 6
}
}
}Limitations and assumptions
Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Weak-Tie Strength Four-Point Scale Tool: Weak-tie strength requires declared observations and an operational definition of tie dimensions. For a complementary comparison, use Political Discussion Network Size Calculator: A discussion-network size counts distinct observed partners of a declared ego.
References
-
Six-Degrees Hop Small-World Estimator — tool.io
Similar or alternative tools
- Weak-Tie Strength Four-Point Scale Tool
Weak-tie strength requires declared observations and an operational definition of tie dimensions.
- Political Discussion Network Size Calculator
A discussion-network size counts distinct observed partners of a declared ego.