Global Transitivity Clustering Ratio Calculator
Actual binary undirected global transitivity3triangles/connected triples; not mean local clustering and disconnected observed nodes retained. No triples leaves ratio undefined and is rejected.
Description
Global transitivity compares closed triangles with connected triples in an undirected graph.
Global transitivity compares closed triangles with connected triples in an undirected graph.1
It differs from equally averaging each node's local clustering coefficient.
When to use Global Transitivity Clustering Ratio Calculator
Use this tool to obtain observedGlobalTransitivity, observedTriangleCount, connectedTripleCount 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 Global Transitivity Clustering Ratio Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter observedAdjacency, using the field meanings and rules below, then run the tool.
- Read result.observedGlobalTransitivity, result.observedTriangleCount, result.connectedTripleCount. 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 |
|---|---|---|---|
| observedAdjacency | Observed adjacency | numeric matrix | Required |
Require an undirected symmetric binary graph of two through 32 nodes without self-loops. Count triangles once over increasing node triplets and connected triples as sum of degree choose two. Require at least one connected triple; return three times triangles divided by triples with both counts.
globalTransitivity=3×triangleCount/Σ(degree_i×(degree_i−1)/2) 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.observedGlobalTransitivity | Three times triangle count divided by connected-triple count. | number |
| result.observedTriangleCount | Number of complete unordered three-node subgraphs. | number |
| result.connectedTripleCount | Sum over nodes of degree choose two, including triples closed by a third edge. | number |
{
"input": {
"observedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
]
},
"output": {
"result": {
"observedGlobalTransitivity": 0,
"observedTriangleCount": 0,
"connectedTripleCount": 1
}
}
}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. Lists and matrices must be dense, without missing cells. Numeric matrices allow at most 128 rows and 128 columns, subject to the narrower shape requirements above. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Directed Graph Reciprocity Rate Calculator: Directed reciprocity compares reciprocated arcs with all observed arcs. For a complementary comparison, use Homophily Assortativity Coefficient Calculator: Categorical assortativity compares observed same-category directed ties with the mixing expected from endpoint marginals.
References
Similar or alternative tools
- Directed Graph Reciprocity Rate Calculator
Directed reciprocity compares reciprocated arcs with all observed arcs.
- Homophily Assortativity Coefficient Calculator
Categorical assortativity compares observed same-category directed ties with the mixing expected from endpoint marginals.