Threshold

The Profile-Threshold model, introduced by Milli et al. in [1], assumes the existence of node profiles that act as preferential schemas for individual tastes but relax the constraints imposed by the Profile model by letting nodes influenceable via peer pressure mechanisms.

The peer pressure is modeled with a threshold.

The diffusion process starts from a set of nodes that have already adopted a given behaviour S:

  • for each of the susceptible node an unbalanced coin is flipped if the percentage of its neighbors that are already infected excedes its threhosld. As in the Profile Model the coin unbalance is given by the personal profile of the susceptible node;
  • if a positive result is obtained the susceptible node will adopt the behaviour, thus becoming infected.
  • if the blocked status is enabled, after having rejected the adoption with probability blocked a node becomes immune to the infection.
  • every iteration adopter_rate percentage of nodes spontaneous became infected to endogenous effects.

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Blocked -1

Parameters

Name Type Value Type Default Mandatory Description
threshold Node float in [0, 1] 0.1 False Individual threshold
profile Node float in [0, 1] 0.1 False Node profile
blocked Model float in [0, 1] 0 False Blocked nodes
adopter_rate Model float in [0, 1] 0 False Autonomous adoption

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.dynamic.DynProfileThresholdModel.DynProfileThresholdModel(graph)

Node Parameters to be specified via ModelConfig

Parameters:
  • profile – The node profile. As default a value of 0.1 is assumed for all nodes.
  • threshold – The node threshold. As default a value of 0.1 is assumed for all nodes.
DynProfileThresholdModel.__init__(graph)

Model Constructor

Parameters:graph – A networkx graph object
DynProfileThresholdModel.set_initial_status(self, configuration)

Set the initial model configuration

Parameters:configuration – a `ndlib.models.ModelConfig.Configuration` object
DynProfileThresholdModel.reset(self)

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

Describe

DynProfileThresholdModel.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
DynProfileThresholdModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

DynProfileThresholdModel.iteration(self)

Execute a single model iteration

Returns:Iteration_id, Incremental node status (dictionary node->status)
DynProfileThresholdModel.execute_snapshots(bunch_size, node_status)

NB: the ``execute_iterations()`` method is unavailable for this model (along with other thresholded models).

Example

In the code below is shown an example of instantiation and execution of a Profile Threshold model simulation on a random graph: we set the initial infected node set to the 10% of the overall population, assign a profile of 0.25 and a threshold of 0.15 to all the nodes.

import networkx as nx
import dynetx as dn
import ndlib.models.ModelConfig as mc
import ndlib.models.dynamic.DynProfileThresholdModel as prTr
from past.builtins import xrange

# Dynamic Network topology
dg = dn.DynGraph()

for t in xrange(0, 3):
    g = nx.erdos_renyi_graph(200, 0.05)
    dg.add_interactions_from(g.edges(), t)

# Model selection
model = prTr.DynProfileThresholdModel(dg)
config = mc.Configuration()
config.add_model_parameter('blocked', 0)
config.add_model_parameter('adopter_rate', 0)
config.add_model_parameter('percentage_infected', 0.1)

# Setting nodes parameters
threshold = 0.15
profile = 0.25
for i in g.nodes():
    config.add_node_configuration("threshold", i, threshold)
    config.add_node_configuration("profile", i, profile)

model.set_initial_status(config)


# Simulate snapshot based execution
iterations = model.execute_snapshots()
[1]Milli, L., Rossetti, G., Pedreschi, D., & Giannotti, F. (2018). Active and passive diffusion processes in complex networks. Applied network science, 3(1), 42.