The Threshold model was introduced in 1978 by Granovetter [1].

In this model during an epidemic, a node has two distinct and mutually exclusive behavioral alternatives, e.g., the decision to do or not do something, to participate or not participate in a riot.

Node’s individual decision depends on the percentage of its neighbors that have made the same choice, thus imposing a threshold.

The model works as follows: - each node has its own threshold; - during a generic iteration every node is observed: if the percentage of its infected neighbors is greater than its threshold it becomes infected as well.


During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1


Name Type Value Type Default Mandatory Description
threshold Node float in [0, 1] 0.1 False Individual threshold

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.


The following class methods are made available to configure, describe and execute the simulation:


class ndlib.models.epidemics.ThresholdModel.ThresholdModel(graph, seed=None)
Node Parameters to be specified via ModelConfig
Parameters:threshold – The node threshold. If not specified otherwise a value of 0.1 is assumed for all nodes.

Model Constructor

Parameters:graph – A networkx graph object
ThresholdModel.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)
ThresholdModel.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 Threshold model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population, and assign a threshold of 0.25 to all the nodes.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics as ep

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

# Model selection
model = ep.ThresholdModel(g)

# Model Configuration
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)

# Setting node parameters
threshold = 0.25
for i in g.nodes():
    config.add_node_configuration("threshold", i, threshold)


# Simulation execution
iterations = model.iteration_bunch(200)
  1. Granovetter, “Threshold models of collective behavior,” The American Journal of Sociology, vol. 83, no. 6, pp. 1420–1443, 1978.