The Weighted Hegselmann-Krause was introduced by Milli et al. in 20211.
This model is a variation of the well-known Hegselmann-Krause (HK). During each interaction a random agenti is selected and the set Γϵ of its neighbors whose opinions differ at most ϵ (di, j = |xi(t) − xj(t)| ≤ ϵ) is identified. Moreover, to account for the heterogeneity of interaction frequency among agent pairs, WHK leverages edge weights, thus capturing the effect of different social bonds' strength/trust as it happens in reality. To such extent, each edge (i, j) ∈ E, carries a value wi, j ∈ [0, 1]. The update rule then becomes:
The idea behind the WHK formulation is that the opinion of agent i at time t + 1, will be given by the combined effect of his previous belief and the average opinion weighed by its, selected, ϵ-neighbor, where wi, j accounts for i's perceived influence/trust of j.
Node statuses are continuous values in [-1,1].
Name | Type | Value Type | Default | Mandatory | Description |
---|---|---|---|---|---|
epsilon | Model | float in [0, 1] |
|
True | Bounded confidence threshold |
perc_stubborness | Model | float in [0, 1] |
|
False | Percentage of stubborn agent |
similarity | Model | int in {0, 1} |
|
False | The method use the feature of the nodes ot not |
option_for_stubbornness | Model | int in {-1,0, 1} |
|
False | Define distribution of stubborns |
weight | Edge | float in [0, 1] |
|
False | Edge weight |
stubborn | Node | int in {0, 1} |
|
False | The agent is stubborn or not |
vector | Node | Vector of float in [0, 1] |
|
False | Vector represents the character of the node |
The following class methods are made available to configure, describe and execute the simulation:
ndlib.models.opinions.WHKModel.WHKModel
ndlib.models.opinions.WHKModel.WHKModel.__init__(graph)
ndlib.models.opinions.WHKModel.WHKModel.set_initial_status(self, configuration)
ndlib.models.opinions.WHKModel.WHKModel.reset(self)
ndlib.models.opinions.WHKModel.WHKModel.get_info(self)
ndlib.models.opinions.WHKModel.WHKModel.get_status_map(self)
ndlib.models.opinions.WHKModel.WHKModel.iteration(self)
ndlib.models.opinions.WHKModel.WHKModel.iteration_bunch(self, bunch_size)
In the code below is shown an example of instantiation and execution of an WHK model simulation on a random graph: we an epsilon value of 0.32 and a weight equal 0.2 to all the edges.
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.WHKModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter("epsilon", 0.32)
# Setting the edge parameters
weight = 0.2
if isinstance(g, nx.Graph):
edges = g.edges
else:
edges = [(g.vs[e.tuple[0]]['name'], g.vs[e.tuple[1]]['name']) for e in g.es]
for e in edges:
config.add_edge_configuration("weight", e, weight)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(20)
- Milli and G. Rossetti. “Opinion Dynamic Modeling of News Perception”.