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:

  • fraction_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:


class ndlib.models.opinions.VoterModel.VoterModel(graph, seed=None)

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

Reset the simulation setting the actual status to the initial configuration.



Describes the current model parameters (nodes, edges, status)

Returns:a dictionary containing for each parameter class the values specified during model configuration

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation


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

  • 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

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 as op

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

# Model selection
model = op.VoterModel(g)
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)


# Simulation execution
iterations = model.iteration_bunch(200)
  1. Clifford and A. Sudbury, “A model for spatial conflict,” Biometrika, vol. 60, no. 3, pp. 581–588, 1973.
  1. Holley and T. Liggett, “Ergodic theorems for weakly interacting infinite systems and the voter model,” Ann. Probab., vol. 3, no. 4, pp. 643–663, Aug 1975.
[3]P.L.Krapivsky,S.Redner,andE.Ben-Naim,Akineticviewofstatistical physics. Cambridge University Press, 2010.