Simmel Dyad-Triad Census Ratio Calculator
Actual undirected dyad/connected-triad census, distinguishing complete and open triads; not directed16-class census or proof of Simmel social dynamics. Unconnected triple sets excluded.
Description
An undirected triad census distinguishes complete triangles from connected two-edge triples.
An undirected triad census distinguishes complete triangles from connected two-edge triples.1
Counting those structures does not constitute the full directed triad census.
When to use Simmel Dyad-Triad Census Ratio Calculator
Use this tool to obtain completeTriadCount, incompleteConnectedTriadCount, observedDyadEdgeCount 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 Simmel Dyad-Triad Census 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.completeTriadCount, result.incompleteConnectedTriadCount, result.observedDyadEdgeCount. 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 a symmetric binary zero-diagonal graph for two through 32 nodes. Traverse each unordered node triplet once: three edges count as complete, exactly two as incomplete connected. Return those counts and total undirected edges; isolated or one-edge triplets do not enter the two triad counts. No ratio or full directed census is returned.
complete=count(triplets with 3 edges); incompleteConnected=count(triplets with 2 edges); dyadEdges=Σadjacency/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.completeTriadCount | Number of unordered triples with all three edges present. | number |
| result.incompleteConnectedTriadCount | Number of unordered triples with exactly two edges present. | number |
| result.observedDyadEdgeCount | Total undirected observed edges, counted once per pair. | number |
{
"input": {
"observedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
]
},
"output": {
"result": {
"completeTriadCount": 0,
"incompleteConnectedTriadCount": 1,
"observedDyadEdgeCount": 2
}
}
}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 Global Transitivity Clustering Ratio Calculator: Global transitivity compares closed triangles with connected triples in an undirected graph. For a complementary comparison, use Structural Hole Redundancy Measure Calculator: Structural-hole redundancy describes ties among an ego's observed alters.
References
Similar or alternative tools
- Global Transitivity Clustering Ratio Calculator
Global transitivity compares closed triangles with connected triples in an undirected graph.
- Structural Hole Redundancy Measure Calculator
Structural-hole redundancy describes ties among an ego's observed alters.