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:

  • percentage_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)

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.
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.QVoterModel as qvt

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

# Model selection
model = qvt.QVoterModel(g)
config = mc.Configuration()
config.add_model_parameter("q", 5)
config.add_model_parameter('percentage_infected', 0.1)

model.set_initial_status(config)

# Simulation execution
iterations = model.iteration_bunch(200)
[1]
  1. Castellano, M. A. Munoz, and R. Pastor-Satorras, “The non-linear q-voter model,” Physical Review E, vol. 80, p. 041129, 2009.