Betweenness Centrality Calculator

Brandesunweighted UNDIRECTED raw node betweenness, shortest path ties fractionally shared, end points excluded, unordered pairs, count not normalized. ≤64nodes, no weighted/directed inference.

Description

Node betweenness measures the share of shortest paths that pass through a node, with tied paths sharing contribution.

Node betweenness measures the share of shortest paths that pass through a node, with tied paths sharing contribution.^[1]

This tool computes raw unweighted undirected betweenness from a supplied adjacency matrix, excluding path endpoints.

When to use Betweenness Centrality Calculator

This tool computes raw unweighted undirected betweenness from a supplied adjacency matrix, excluding path endpoints.

How to use Betweenness Centrality Calculator and how it works

Prepare unweighted undirected adjacency, using the input definitions and matching units below.
Enter the required fields and run Betweenness Centrality Calculator.
Read result.rawNodeBetweenness using the 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	Binary symmetric square adjacency matrix, zero diagonal, at most 64 nodes.	array of array of number	Required; other constraints below

Require a nonempty square adjacency matrix of at most 64 nodes with binary entries, symmetry and zero diagonal. Use breadth-first shortest-path discovery from every source, record predecessor paths and counts, and accumulate Brandes dependencies sharing tied paths fractionally. Exclude endpoints and divide totals by two for unordered node pairs. Return raw node scores in matrix order; disconnected pairs contribute zero and no normalization or weighted/directed branch is applied.

rawBetweenness(v)=sum_over_unordered_s_t(sigma_st(v)/sigma_st)

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.rawNodeBetweenness	Raw unordered-pair shortest-path contribution scores in adjacency-node order.	array of number

json

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

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 Synchrony Index Calculator for a complementary operation: Circular vector strength measures how concentrated assigned spike phases are around a common direction.

Use Mean Firing Rate Calculator for a complementary operation: Mean firing rate summarizes total observed spikes over the full recording exposure.

References

Betweenness Centrality Calculator — tool.io

Similar or alternative tools

Synchrony Index Calculator
Circular vector strength measures how concentrated assigned spike phases are around a common direction.
Mean Firing Rate Calculator
Mean firing rate summarizes total observed spikes over the full recording exposure.