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:
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 |
Methods¶
The following class methods are made available to configure, describe and execute the simulation:
Configure¶
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class
ndlib.models.opinions.HKModel.HKModel(graph)¶ Model Parameters to be specified via ModelConfig :param epsilon: bounded confidence threshold from the HK model (float in [0,1])
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HKModel.__init__(graph)¶ Model Constructor :param graph: A networkx graph object
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HKModel.set_initial_status(self, configuration)¶ Override behaviour of methods in class DiffusionModel. Overwrites initial status using random real values.
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HKModel.reset(self)¶ Reset the simulation setting the actual status to the initial configuration.
Describe¶
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HKModel.get_info(self)¶ Describes the current model parameters (nodes, edges, status)
Returns: a dictionary containing for each parameter class the values specified during model configuration
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HKModel.get_status_map(self)¶ Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Execute Simulation¶
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HKModel.iteration(self)¶ Execute a single model iteration
Returns: Iteration_id, Incremental node status (dictionary code -> status)
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HKModel.iteration_bunch(self, bunch_size)¶ Execute a bunch of model iterations
Parameters: - bunch_size – the number of iterations to execute
- node_status – if the incremental node status has to be returned.
- progress_bar – whether to display a progress bar, default False
Returns: a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}
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)
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