Kertesz Threshold¶
The Kertesz Threshold model was introduced in 2015 by Ruan et al. [1] and it is an extension of the Watts threshold model [2].
The authors extend the classical model introducing a density r of blocked nodes – nodes which are immune to social influence – and a probability of spontaneous adoption p to capture external influence.
Thus, the model distinguishes three kinds of node: Blocked (B), Susceptible (S) and Adoptiong (A). The latter class breaks into two categories: vulnerable and stable nodes. A node can adopt either under its neighbors’ influence, or spontaneously, due 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 |
|---|---|---|---|---|---|
| adopter_rate | Model | float in [0, 1] | 0 | False | Exogenous adoption rate |
| percentage_blocked | Model | float in [0, 1] | 0.1 | False | Blocked nodes |
| 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 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.
Methods¶
The following class methods are made available to configure, describe and execute the simulation:
Configure¶
-
class
ndlib.models.dynamic.DynKerteszThresholdModel.DynKerteszThresholdModel(graph, seed=None)¶ - Node Parameters to be specified via ModelConfig
Parameters: profile – The node profile. As default a value of 0.1 is assumed for all nodes.
-
DynKerteszThresholdModel.__init__(graph)¶ Model Constructor
Parameters: graph – A networkx graph object
-
DynKerteszThresholdModel.set_initial_status(self, configuration)¶ Set the initial model configuration
Parameters: configuration – a `ndlib.models.ModelConfig.Configuration`object
-
DynKerteszThresholdModel.reset(self)¶ Reset the simulation setting the actual status to the initial configuration.
Describe¶
-
DynKerteszThresholdModel.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
-
DynKerteszThresholdModel.get_status_map(self)¶ Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Example¶
In the code below is shown an example of instantiation and execution of a Kertesz Threshold model simulation on a random graph: we set the initial infected as well blocked node sets equals to the 10% of the overall population, assign a threshold of 0.25 to all the nodes and impose an probability of spontaneous adoptions of 40%.
import networkx as nx
import dynetx as dn
import ndlib.models.ModelConfig as mc
import ndlib.models.dynamic as dm
# Dynamic Network topology
dg = dn.DynGraph()
for t in past.builtins.xrange(0, 3):
g = nx.erdos_renyi_graph(200, 0.05)
dg.add_interactions_from(g.edges(), t)
# Model selection
model = dm.DynKerteszThresholdModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('adopter_rate', 0.4)
config.add_model_parameter('percentage_blocked', 0.1)
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)
model.set_initial_status(config)
# Simulate snapshot based execution
iterations = model.execute_snapshots()
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