Hegselmann-Krause¶

The Hegselmann-Krause model was introduced in 2002 by Hegselmann, Krause et al [1].

During each interaction a random agenti is selected and the set \(\Gamma_{\epsilon}\) of its neighbors whose opinions differ at most \(\epsilon\) (\(d_{i,j}=|x_i(t)-x_j(t)|\leq \epsilon\)) is identified. The selected agent i changes its opinion based on the following update rule:

\[x_i(t+1)= \frac{\sum_{j \in \Gamma_{\epsilon}} x_j(t)}{\#\Gamma_{\epsilon}}\]

The idea behind the WHK formulation is that the opinion of agent \(i\) at time \(t+1\), will be given by the average opinion by its, selected, \(\epsilon\)-neighbor.

Statuses¶

Node statuses are continuous values in [-1,1].

Parameters¶

Name	Type	Value Type	Default	Mandatory	Description
epsilon	Model	float in [0, 1]	—	True	Bounded confidence threshold

Example¶

In the code below is shown an example of instantiation and execution of an HK model simulation on a random graph: we an epsilon value of 0.32 .

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.opinions as opn

# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)

# Model selection
model = opn.HKModel(g)

# Model Configuration
config = mc.Configuration()
config.add_model_parameter("epsilon", 0.32)

model.set_initial_status(config)

# Simulation execution
iterations = model.iteration_bunch(20)