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.
Methods¶
The following class methods are made available to configure, describe and execute the simulation:
Configure¶
-
class
ndlib.models.opinions.QVoterModel.QVoterModel(graph, seed=None)¶ Node Parameters to be specified via ModelConfig
Parameters: q – the number of neighbors that affect the opinion of a node
-
QVoterModel.__init__(graph)¶ Model Constructor
Parameters: graph – A networkx graph object
-
QVoterModel.set_initial_status(self, configuration)¶ Set the initial model configuration
Parameters: configuration – a `ndlib.models.ModelConfig.Configuration`object
-
QVoterModel.reset(self)¶ Reset the simulation setting the actual status to the initial configuration.
Describe¶
-
QVoterModel.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
-
QVoterModel.get_status_map(self)¶ Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Execute Simulation¶
-
QVoterModel.iteration(self)¶ Execute a single model iteration
Returns: Iteration_id, Incremental node status (dictionary node->status)
-
QVoterModel.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 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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