Q-Voter¶
The Q-Voter model was introduced as a generalisation of discrete opinion dynamics models [1].
Here, N individuals hold an opinion ±1. At each time step, a set of q neighbours are chosen and, if they agree, they influence one neighbour chosen at random, i.e. this agent copies the opinion of the group. If the group does not agree, the agent flips its opinion with probability ε.
It is clear that the voter and Sznajd models are special cases of this more recent model (q = 1,ε = 0 and q = 2,ε = 0).
Analytic results for q ≤ 3 validate the numerical results obtained for the special case models, with transitions from a ordered phase (small ε) to a disordered one (large ε). For q > 3, a new type of transition between the two phases appears, which consist of passing through an intermediate regime where the final state depends on the initial condition. We implemented in NDlib the model with ε = 0.
Statuses¶
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
Parameters¶
| Name | Type | Value Type | Default | Mandatory | Description |
|---|---|---|---|---|---|
| q | Model | int in [0, V(G)] | True | Number of neighbours |
The initial infection status can be defined via:
- fraction_infected: Model Parameter, float in [0, 1]
- Infected: Status Parameter, set of nodes
The two options are mutually exclusive and the latter takes precedence over the former.
Example¶
In the code below is shown an example of instantiation and execution of a Q-Voter model simulation on a random graph: we set the initial infected node set to the 10% of the overall population and the number q of influencing neighbors equals to 5.
import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.opinions as op
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = op.QVoterModel(g)
config = mc.Configuration()
config.add_model_parameter("q", 5)
config.add_model_parameter('fraction_infected', 0.1)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
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