1.0.5 • Public • Published

Basic Influence Roles (BIRs) · GitHub license PRs Welcome

Detect and measure the basic role of influence each node plays within a directed network.

It supports a raw list of nodes, a Graphology DiGraph, as well as a method to be used in a distributed context for Big Data use cases.

This algorithm returns:

  • The Basic Influence Role (BIR) of a node in a network
  • The BIR's level
  • The influence measure related to the role
  • A global influence measure based on indegree and outdegree
  • The influence ranking of the node

For in-depth theoretical details and more examples, please read the main repository intro.

Index of contents

All useful informations can be found in the following paragraphs:


npm install basic-influence-roles

How to use it

Import BIRs package

Using import:

import BIRs from 'basic-influence-roles';

Using require:

const BIRs = require('basic-influence-roles');

Detect Basic Influence Roles

Methods to detect BIRs.

From a list of nodes



Field Type Required Description
nodes [{...}] yes An array of all nodes' data.
nodes[i].id any yes The name or id of the node.
nodes[i].indegree integer yes The number of incoming connections.
nodes[i].outdegree integer yes The number of outcoming connections.
// The list of nodes with indegree and outdegree
nodes = [
  {id: 1, indegree: 13, outdegree: 5},
  {id: 2, indegree: 3, outdegree: 8},
  {id: 3, indegree: 0, outdegree: 22},
  {id: 4, indegree: 16, outdegree: 19},
// Measure the influence score and detect the basic influence roles
res = BIRs.detectFromNodes(nodes);

From a Graphology directed graph

Detect roles of a Graphology Directed Graph



Type Required Description
G yes A Graphology directed graph.
const { DirectedGraph } = require('graphology');
// Create a directed graph
const G = new DirectedGraph({multi: false, allowSelfLoops: false});
// Add some nodes and edges
// Detect basic influence roles of nodes
res = BIRs.detectGraphology(G);

To use in a distributed context

In case of Big Data or Huge Networks you can distribute the load in this way:

BIRs.detect(indegree, outdegree, nodeCount, data);


Field Type Required Description
indegree integer yes The number of incoming connections.
outdegree integer yes The number of outcoming connections.
nodeCount integer yes The total number of nodes.
data boolean no If true returns indegree and outdegree.
// Get the total count of nodes
nodeCount = 8586987087;
// For every node in a huge network (use here a distributed loop instead)[indegree, outdegree]) => {
    // Get basic influence role of every node in network
    return BIRs.detect(indegree, outdegree, nodeCount, true);


The output is a list of nodes reporting their id, role, role level, influence measure, influence ranking.

Field Type Description
id any The id of node.
role string The basic influence role.
roleInfluence float The influence magnitude related to the node's role.
roleLevel string The level of role, a role subcategory.
influence float A normalized influence score based on indegree and outdegree.
indegree integer The number of incoming connections.
outdegree integer The number of outcoming connections.
normalizedIndegree float The normalized number of incoming connections.
normalizedOutdegree float The normalized number of outcoming connections.
rank integer The normalized influence ranking based on the value of influence field.
        id: 4,
        role: 'hub',
        roleInfluence: 0.9210526315789473,
        roleLevel: 'strong',
        influence: 0.9210526315789473,
        indegree: 16,
        outdegree: 19,
        normalizedIndegree: 0.8421052631578947,
        normalizedOutdegree: 1.0,
        rank: 1
        id: 3,
        role: 'emitter',
        roleInfluence: 0.9473684210526315,
        roleLevel: 'strong',
        influence: 0.47368421052631576,
        indegree: 0,
        outdegree: 18,
        normalizedIndegree: 0.0,
        normalizedOutdegree: 0.9473684210526315
        rank: 2

Get the distribution of Basic Influence Roles

Given a list of BIRs, can be calculated the distribution of BIRs in a network, as a normalized frequency between roles and also between their levels.



Field Type Required Description
data [{...}] yes The list of roles, the output of BIRs' detection methods.
// Detect basic influence roles of nodes
data = BIRs.detectFromNodes([...])
// Detect the distribution of BIRs
res = BIRs.distribution(data)


    reducer: {
        count: 12,
        frequency: 0.12,
        levels: {
            none: {count: 0, frequency: 0.0},
            branch: {count: 0, frequency: 0.0},
            weak: {count: 7, frequency: 0.07},
            strong: {count: 5, frequency: 0.05},
            top: {count: 0, frequency: 0.0}
    amplifier: {
        count: 13,
        frequency: 0.13,
        levels: {
            none: {count: 0, frequency: 0.0},
            branch: {count: 0, frequency: 0.0},
            weak: {count: 12, frequency: 0.12},
            strong: {count: 1, frequency: 0.01},
            top: {count: 0, frequency: 0.0}
    emitter: {
        count: 28,
        frequency: 0.28,
        levels: {
            none: {count: 0, frequency: 0.0},
            branch: {count: 18, frequency: 0.18},
            weak: {count: 10, frequency: 0.1},
            strong: {count: 0, frequency: 0.0},
            top: {count: 0, frequency: 0.0}


The package is battle tested with a coverage of 98%. Unit tests are inside the folder /test.

At first, install dev requirements:

npm install

To run all unit tests with coverage through nyc, type:

npm test


If you use this software in your work, please cite it as below:

Miceli, D. (2024). Basic Influence Roles (BIRs) [Computer software].

Or the BibTeX version:

  author = {Miceli, Davide},
  license = {MIT},
  month = mar,
  title = {{Basic Influence Roles (BIRs)}},
  url = {},
  year = {2024}


Basic Influence Roles is an open source project available under the MIT license.

Package Sidebar


npm i basic-influence-roles

Weekly Downloads






Unpacked Size

14.5 kB

Total Files


Last publish


  • davidemiceli