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Independent Cascades
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The Independent Cascades model was introduced by Kempe et all in 2003 [#]_. 

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.

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Statuses
--------

During the simulation a node can experience the following statuses:

===========  ====
Name         Code
===========  ====
Susceptible  0
Infected     1
Removed      2
===========  ====


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Parameters
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==============  =====  ===============  =======  =========  ==============
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.

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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.


.. code-block:: python

    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)


.. [#] D. Kempe, J. Kleinberg, and E. Tardos, “Maximizing the spread of influence through a social network,” in Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ser. KDD ’03, 2003, pp. 137–146.