Closeness Sociology Calculator
Explicit normalized HARMONIC closenessΣ1/d/(N−1), unreachable vertices zero not artificial finite path. Actual binary undirected simple graph, not conventional closeness with implicit connectedness.
Description
Harmonic closeness summarizes reciprocal shortest-path distances from each node.
Harmonic closeness summarizes reciprocal shortest-path distances from each node.1
Unreachable nodes contribute zero, allowing a defined measure on disconnected networks. The calculation and input requirements are explained below.
When to use Closeness Sociology Calculator
Enter a symmetric binary square adjacency matrix with zero diagonal and 2–64 nodes.
How to use Closeness Sociology Calculator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Closeness Sociology Calculator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualUnweightedUndirectedAdjacency | Actual Unweighted Undirected Adjacency. Use the units and matching context stated in the calculation below. | array of array of number | Required; other constraints below |
Enter a symmetric binary square adjacency matrix with zero diagonal and 2–64 nodes. Breadth-first search supplies shortest paths from each node. Sum reciprocals of positive distances and divide by N-1; self-distances and unreachable nodes contribute zero. Output follows input node order.
harmonicCloseness_i=sum(reciprocalReachableDistances_i)/(N-1) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.observedHarmonicCloseness | Observed Harmonic Closeness. Interpret its unit, sign, order or availability flag as explained above. | array of number |
{
"input": {
"actualUnweightedUndirectedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
]
},
"output": {
"result": {
"observedHarmonicCloseness": [
0.75,
1,
0.75
]
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Network Density Sociology Calculator for a complementary operation: Network density describes the proportion of possible ties that are observed.
Use Degree Centralization Calculator for a complementary operation: Freeman degree centralization compares every node's degree with the maximum degree.
References
-
Closeness Sociology Calculator — tool.io
Similar or alternative tools
- Network Density Sociology Calculator
Network density describes the proportion of possible ties that are observed.
- Degree Centralization Calculator
Freeman degree centralization compares every node's degree with the maximum degree.