Pathway Betweenness

Calculate undirected pathway graph betweenness by shortest-path dependency.

Description

Betweenness centrality measures how often a node lies on shortest paths between other nodes.

Betweenness centrality measures how often a node lies on shortest paths between other nodes. This implementation treats the network as undirected and unweighted.^[1]

Calculate undirected pathway graph betweenness by shortest-path dependency.

When to use Pathway Betweenness

Use this tool to calculate undirected pathway graph betweenness by shortest-path dependency.

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.

How to use Pathway Betweenness and understand its results

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.
Enter nodeIds, adjacency using the field table and calculation rules, then run the tool.
Read betweenness, topNodeId. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
nodeIds	Node ids	list of string	Required
adjacency	Adjacency	list of list of number	Required

Enter at least three node IDs and a matching square symmetric binary adjacency matrix with zero diagonal. Use breadth-first shortest paths and reverse dependency accumulation from each node, then halve scores for undirected counting. Return raw scores and first highest-scoring ID.

centrality(v)=Σ unordered s,t σ_st(v)/σ_st

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
betweenness	Betweenness	list of number
topNodeId	Top node id	string

json

{
  "input": {
    "nodeIds": [
      "a",
      "b",
      "c"
    ],
    "adjacency": [
      [
        0,
        1,
        0
      ],
      [
        1,
        0,
        1
      ],
      [
        0,
        1,
        0
      ]
    ]
  },
  "output": {
    "betweenness": [
      0,
      1,
      0
    ],
    "topNodeId": "b"
  }
}

Limitations and assumptions

Scores are not normalized. IDs need not be unique; no weighted or directed edges, pathway annotation or causal influence is modeled.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Pathway Overrepresentation: Calculate hypergeometric pathway over-representation and upper-tail probability. For a complementary task, use Stoichiometric Flux Balance: Check S·v steady-state residuals against a supplied flux-balance tolerance.

References

Pathway Betweenness — tool.io

Similar or alternative tools

Pathway Overrepresentation
Calculate hypergeometric pathway over-representation and upper-tail probability.
Stoichiometric Flux Balance
Check S·v steady-state residuals against a supplied flux-balance tolerance.