FJsim 1.1

A module capable of simulating the spreading of an opinon in a given network using the Friedkin-Johnsen model.

Friedkin-Johnsen-model-simulator

A module capable of simulating the spreading of an opinon in a given network using the Friedkin-Johnsen model.

Table of contents

• Requirements
• Installation
• Usage
• Example

Requirements

• Python 3.9.10 or higher
• Numpy 1.25.0 or higher

Installation

Clone the repository:

git clone https://github.com/Giorgio-ctrl/Friedkin-Johnsen-model-simulator.git

or install via pip:

python -m pip install FJsim

Usage

model = Friedkin_Johnsen(weight, influence)

• weight is the stochastic weighed adjacency matrix of the network (each element a_ij is the influence of node j on node i)
• influence is the matrix where each diagonal element is how much a node is influenced by others and all the other entries are 0

model.simulate(initial)

• initial is the nx1 vector of the original opions of each node

This code altogether returns the opinions that the system converges to or -1 if they don't converge.

Example

weight = numpy.array([
              [0.220, 0.120, 0.360, 0.300],
              [0.147, 0.215, 0.344, 0.294],
              [0.000, 0.000, 1.000, 0.000],
              [0.090, 0.178, 0.446, 0.286]
              ])
influence = numpy.diag([0.780, 0.785, 0, 0.714])
initial = numpy.transpose([25, 25, 75, 85])

model = Friedkin_Johnsen(weight, influence)
print(model.simulate(initial)

This code will print:

[60.02084883 59.98396594 75.         74.98620494]

Which is exactly the vector of the opinions once they converge.