Burt Network Constraint Efficiency Calculator
Actual binary undirected ego network Burt-style constraint summed over direct alters and effective-size efficiency1−2t/k². Explicit equal tie weights; not weighted-network convention, causal brokerage or universal social-capital ranking.
Description
Ego network constraint measures direct and indirect dependence under an adopted tie normalization.
Ego network constraint measures direct and indirect dependence under an adopted tie normalization.1
Efficiency uses ties among the ego's neighbors in this simplified unweighted graph convention.
When to use Burt Network Constraint Efficiency Calculator
Use this tool to obtain observedEgoConstraint, observedEgoEfficiency 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 Burt Network Constraint Efficiency Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter observedAdjacency, egoNodeIndex, using the field meanings and rules below, then run the tool.
- Read result.observedEgoConstraint, result.observedEgoEfficiency. 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 |
| egoNodeIndex | Ego node index | number | Required |
Require a symmetric binary zero-diagonal graph for two through 32 nodes and an integer ego index in its range. Ego must have at least one neighbor. Normalize each node's ties by its degree, using zero rows for isolates. For each ego neighbor square direct proportional tie plus indirect contributions through other nodes, then sum. Separately count ties among ego neighbors for the declared efficiency formula. This is the simplified unweighted convention, not a weighted relation model.
constraint_i=Σneighbors_j(p_ij+Σq≠i,j(p_iq×p_qj))²; efficiency=1−2×alterTieCount/egoDegree² 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.observedEgoConstraint | Sum over ego neighbors of squared direct-plus-indirect proportional dependence. | number |
| result.observedEgoEfficiency | One minus two times ties among ego neighbors divided by squared ego degree. | number |
{
"input": {
"observedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
],
"egoNodeIndex": 1
},
"output": {
"result": {
"observedEgoConstraint": 0.5,
"observedEgoEfficiency": 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 Structural Hole Redundancy Measure Calculator: Structural-hole redundancy describes ties among an ego's observed alters. For a complementary comparison, use Bridging/Bonding Capital Ratio Calculator: Bridging and bonding counts depend on independently established tie categories.
References
Similar or alternative tools
- Structural Hole Redundancy Measure Calculator
Structural-hole redundancy describes ties among an ego's observed alters.
- Bridging/Bonding Capital Ratio Calculator
Bridging and bonding counts depend on independently established tie categories.