Network Density Sociology Calculator

Undirected binary simple graph tie density2E/[N(N−1)], actual observed network, no inferred political/social ties.

Description

Network density describes the proportion of possible ties that are observed.

Network density describes the proportion of possible ties that are observed.^[1]

The simple undirected convention counts each tie once and excludes self-loops. The calculation and input requirements are explained below.

When to use Network Density Sociology Calculator

Enter a symmetric binary square adjacency matrix with zero diagonal and 2–64 nodes.

How to use Network Density 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 Network Density 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. Validate the graph, sum matrix entries and divide by N(N-1). Each undirected tie appears twice, giving the fraction of possible ties observed.

density=sum(adjacency)/(N*(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.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": 0.6666666666666666
    }
  }
}

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

Use Degree Centralization Calculator for a complementary operation: Freeman degree centralization compares every node's degree with the maximum degree.

References

Network Density Sociology Calculator — tool.io

Similar or alternative tools

Closeness Sociology Calculator
Harmonic closeness summarizes reciprocal shortest-path distances from each node.
Degree Centralization Calculator
Freeman degree centralization compares every node's degree with the maximum degree.