Degree Centralization Calculator

Freeman undirected degree centralizationΣ(max degree−degree)/[(N−1)(N−2)], N≥3, actual simple binary graph; not normalized individual degree only.

Description

Freeman degree centralization compares every node's degree with the maximum degree.

Freeman degree centralization compares every node's degree with the maximum degree.^[1]

Its normalization uses the maximum possible contrast for a simple undirected network of that size. The calculation and input requirements are explained below.

When to use Degree Centralization Calculator

Enter a symmetric binary square adjacency matrix with zero diagonal and 3–64 nodes.

How to use Degree Centralization 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 Degree Centralization 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 3–64 nodes. Compute each degree as its row sum, sum maximum-degree minus degree over nodes and divide by (N-1)(N-2). A star returns one; a regular network returns zero.

centralization=sum(maxDegree-degree)/((N-1)*(N-2))

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.value	Numeric result under the formula and output units explained above.	number

json

{
  "input": {
    "actualUnweightedUndirectedAdjacency": [
      [
        0,
        1,
        0
      ],
      [
        1,
        0,
        1
      ],
      [
        0,
        1,
        0
      ]
    ]
  },
  "output": {
    "result": {
      "value": 1
    }
  }
}

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 Closeness Sociology Calculator for a complementary operation: Harmonic closeness summarizes reciprocal shortest-path distances from each node.

References

Degree Centralization Calculator — tool.io

Similar or alternative tools

Network Density Sociology Calculator
Network density describes the proportion of possible ties that are observed.
Closeness Sociology Calculator
Harmonic closeness summarizes reciprocal shortest-path distances from each node.