General Threshold¶
The General Threshold model was introduced in 20003 by Kempe [1].
In this model, during an epidemics, a is allowed to change its status from Susceptible to Infected.
The model is instantiated on a graph having a non-empty set of infected nodes.
The model is defined as follows:
At time t nodes become Infected if the sum of the weight of the infected neighbors is greater than the threshold
Statuses¶
During the simulation a node can experience the following statuses:
Name | Code |
---|---|
Susceptible | 0 |
Infected | 1 |
Parameters¶
Name | Type | Value Type | Default | Mandatory | Description |
---|---|---|---|---|---|
threshold | Node | float in [0, 1] | 0.1 | False | Individual threshold |
weight | Edge | float in [0, 1] | 0.1 | False | Edge weight |
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.
Methods¶
The following class methods are made available to configure, describe and execute the simulation:
Configure¶
-
class
ndlib.models.epidemics.GeneralThresholdModel.
GeneralThresholdModel
(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.
- weight – The edge weight. If not specified otherwise a value of 0.1 is assumed for all edges.
-
GeneralThresholdModel.
__init__
(graph)¶ Model Constructor
Parameters: graph – A networkx graph object
-
GeneralThresholdModel.
set_initial_status
(self, configuration)¶ Set the initial model configuration
Parameters: configuration – a `ndlib.models.ModelConfig.Configuration`
object
-
GeneralThresholdModel.
reset
(self)¶ Reset the simulation setting the actual status to the initial configuration.
Describe¶
-
GeneralThresholdModel.
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
-
GeneralThresholdModel.
get_status_map
(self)¶ Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Execute Simulation¶
-
GeneralThresholdModel.
iteration
(self)¶ Execute a single model iteration
Returns: Iteration_id, Incremental node status (dictionary node->status)
-
GeneralThresholdModel.
iteration_bunch
(self, bunch_size)¶ Execute a bunch of model iterations
Parameters: - 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
Returns: a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}
Example¶
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 = epd.GeneralThresholdModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)
# Setting node and edges parameters
threshold = 0.25
weight = 0.2
if isinstance(g, nx.Graph):
nodes = g.nodes
edges = g.edges
else:
nodes = g.vs['name']
edges = [(g.vs[e.tuple[0]]['name'], g.vs[e.tuple[1]]['name']) for e in g.es]
for i in nodes:
config.add_node_configuration("threshold", i, threshold)
for e in edges:
config.add_edge_configuration("weight", e, weight)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
[1] | János Török and János Kertész “Cascading collapse of online social networks” Scientific reports, vol. 7 no. 1, 2017 David Kempe , Jon Kleinberg, and Éva Tardos. “Maximizing the spread of influence through a social network.” Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2003. |