The Voter model is one of the simplest models of opinion dynamics, originally introduced to analyse competition of species and soon after applied to model elections .
The Voter model is one of the simplest models of opinion dynamics, originally introduced to analyse competition of species [1] and soon after applied to model elections [2].
The model assumes the opinion of an individual to be a discrete variable ±1.
The state of the population varies based on a very simple update rule: at each iteration, a random individual is selected, who then copies the opinion of one random neighbour.
Starting from any initial configuration, on a complete network the entire population converges to consensus on one of the two options. The probability that consensus is reached on opinion +1 is equal to the initial fraction of individuals holding that opinion [3].
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
The initial infection status can be defined via:
- percentage_infected: Model Parameter, float in [0, 1]
- Infected: Status Parameter, set of nodes
The initial blocked nodes can be defined via:
- percentage_blocked: Model Parameter, float in [0, 1]
- Blocked: Status Parameter, set of nodes
In both cases, the two options are mutually exclusive and the latter takes precedence over the former.
The following class methods are made available to configure, describe and execute the simulation:
ndlib.models.opinions.VoterModel.VoterModel(graph)VoterModel.__init__(graph)Model Constructor
| Parameters: | graph – A networkx graph object |
|---|
VoterModel.set_initial_status(self, configuration)Set the initial model configuration
| Parameters: | configuration – a `ndlib.models.ModelConfig.Configuration`object |
|---|
VoterModel.reset(self)Reset the simulation setting the actual status to the initial configuration.
VoterModel.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 |
|---|
VoterModel.get_status_map(self)Specify the statuses allowed by the model and their numeric code
| Returns: | a dictionary (status->code) |
|---|
VoterModel.iteration(self)Execute a single model iteration
| Returns: | Iteration_id, Incremental node status (dictionary node->status) |
|---|
VoterModel.iteration_bunch(self, bunch_size)Execute a bunch of model iterations
| Parameters: |
|
|---|---|
| Returns: |
a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status} |
In the code below is shown an example of instantiation and execution of a Voter model simulation on a random graph: we set the initial infected node set to the 10% of the overall population.
import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.opinions.VoterModel as vt
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = vt.VoterModel(g)
config = mc.Configuration()
config.add_model_parameter('percentage_infected', 0.1)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
The Voter model is one of the simplest models of opinion dynamics, originally introduced to analyse competition of species and soon after applied to model elections .
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