Independent Cascades¶
The Independent Cascades model was introduced by Kempe et all in 2003 [1].
This model starts with an initial set of active nodes A0: the diffusive process unfolds in discrete steps according to the following randomized rule:
- When node v becomes active in step t, it is given a single chance to activate each currently inactive neighbor w; it succeeds with a probability p(v,w).
- If w has multiple newly activated neighbors, their attempts are sequenced in an arbitrary order.
- If v succeeds, then w will become active in step t + 1; but whether or not v succeeds, it cannot make any further attempts to activate w in subsequent rounds.
- The process runs until no more activations are possible.
Statuses¶
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
| Removed | 2 |
Parameters¶
| Name | Type | Value Type | Default | Mandatory | Description |
|---|---|---|---|---|---|
| Edge threshold | Edge | float in [0, 1] | 0.1 | False | Edge 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.
Methods¶
The following class methods are made available to configure, describe and execute the simulation:
Configure¶
-
class
ndlib.models.epidemics.IndependentCascadesModel.IndependentCascadesModel(graph, seed=None)¶ Edge Parameters to be specified via ModelConfig
Parameters: threshold – The edge threshold. As default a value of 0.1 is assumed for all edges.
-
IndependentCascadesModel.__init__(graph)¶ Model Constructor
Parameters: graph – A networkx graph object
-
IndependentCascadesModel.set_initial_status(self, configuration)¶ Set the initial model configuration
Parameters: configuration – a `ndlib.models.ModelConfig.Configuration`object
-
IndependentCascadesModel.reset(self)¶ Reset the simulation setting the actual status to the initial configuration.
Describe¶
-
IndependentCascadesModel.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
-
IndependentCascadesModel.get_status_map(self)¶ Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Execute Simulation¶
-
IndependentCascadesModel.iteration(self)¶ Execute a single model iteration
Returns: Iteration_id, Incremental node status (dictionary node->status)
-
IndependentCascadesModel.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 an Independent Cascades 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 0.1 to all the edges.
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.IndependentCascadesModel(g)
# Model Configuration
config = mc.Configuration()
config.add_model_parameter('fraction_infected', 0.1)
# Setting the edge parameters
threshold = 0.1
for e in g.edges():
config.add_edge_configuration("threshold", e, threshold)
model.set_initial_status(config)
# Simulation execution
iterations = model.iteration_bunch(200)
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