Directed Graph Reciprocity Rate Calculator
Directed arc reciprocity:reciprocated directed arcs divided by all observed directed arcs, not reciprocal dyads/all dyads. No self-loops or unobserved-contact inference.
Description
Directed reciprocity compares reciprocated arcs with all observed arcs.
Directed reciprocity compares reciprocated arcs with all observed arcs.1
A mutual dyad contributes two reciprocated arcs under this arc-based convention.
When to use Directed Graph Reciprocity Rate Calculator
Use this tool to obtain observedDirectedArcReciprocity, reciprocatedArcCount, totalObservedArcCount 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 Directed Graph Reciprocity Rate Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter observedDirectedAdjacency, using the field meanings and rules below, then run the tool.
- Read result.observedDirectedArcReciprocity, result.reciprocatedArcCount, result.totalObservedArcCount. 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 |
|---|---|---|---|
| observedDirectedAdjacency | Observed directed adjacency | numeric matrix | Required |
Require a binary directed square adjacency matrix for two through 32 nodes, with no self-loops and positive total arc count. Count each arc whose reverse also exists, then divide by all arcs. A mutual dyad contributes two to numerator and denominator; an empty graph fails.
reciprocity=Σ(a_ij×a_ji)/Σa_ij 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.observedDirectedArcReciprocity | Reciprocated arcs divided by all observed arcs. | number |
| result.reciprocatedArcCount | Arc count with an observed reverse arc; a mutual dyad contributes two. | number |
| result.totalObservedArcCount | Total ones in the directed adjacency matrix. | number |
{
"input": {
"observedDirectedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
0,
0
]
]
},
"output": {
"result": {
"observedDirectedArcReciprocity": 0.6666666666666666,
"reciprocatedArcCount": 2,
"totalObservedArcCount": 3
}
}
}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 Homophily Assortativity Coefficient Calculator: Categorical assortativity compares observed same-category directed ties with the mixing expected from endpoint marginals. For a complementary comparison, use Global Transitivity Clustering Ratio Calculator: Global transitivity compares closed triangles with connected triples in an undirected graph.
References
Similar or alternative tools
- Homophily Assortativity Coefficient Calculator
Categorical assortativity compares observed same-category directed ties with the mixing expected from endpoint marginals.
- Global Transitivity Clustering Ratio Calculator
Global transitivity compares closed triangles with connected triples in an undirected graph.