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fix ICE and ICEP Model and add docs for ICE, ICP and ICEP model
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‎docs/reference/models/epidemics/ICE.rst

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**************************************************
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Independent Cascades with Community Embeddedness
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**************************************************
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The Independent Cascades with Community Embeddedness model was introduced by Milli and Rossetti in 2019 [#]_.
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This model is a variation of the well-known Independent Cascade (IC), and it is designed to embed community awareness into the IC model.
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The probability p(u,v) of the IC model is replaced by the edge embeddedness.
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The embeddedness of an edge :math:`(u,v)` with :math:`u,v \in C` is defined as:
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:math:`e_{u,v} = \frac{\phi_{u,v}}{|\Gamma(u) \cup \Gamma(v)|}`
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where :math:`\phi_{u,v}` is the number of common neighbors of u and v within :math:`C`, and :math:`\Gamma(u)` ( :math:`\Gamma(v)`) is the set of neighbors of the node u (v) in the analyzed graph G.
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The ICE model starts with an initial set of **active** nodes A0; the diffusive process unfolds in discrete steps according to the following randomized rule:
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- When node v becomes active in step t, it is given a single chance to activate each currently inactive neighbor u. If v and u belong to the same community, it succeeds with a probability :math:`e_{u,v}`; otherwise with probability :math:`\min\{e_{z,v}|(z, v)\in E\}`.
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- If u has multiple newly activated neighbors, their attempts are sequenced in an arbitrary order.
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- If v succeeds, then u will become active in step t + 1; but whether or not v succeeds, it cannot make any further attempts to activate u in subsequent rounds.
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- The process runs until no more activations are possible.
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--------
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Statuses
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--------
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During the simulation a node can experience the following statuses:
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=========== ====
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Name Code
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=========== ====
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Susceptible 0
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Infected 1
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Removed 2
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=========== ====
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----------
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Parameters
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----------
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The model is parameter free
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The initial infection status can be defined via:
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- **fraction_infected**: Model Parameter, float in [0, 1]
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- **Infected**: Status Parameter, set of nodes
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The two options are mutually exclusive and the latter takes precedence over the former.
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-------
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Methods
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-------
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The following class methods are made available to configure, describe and execute the simulation:
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^^^^^^^^^
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Configure
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^^^^^^^^^
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.. autoclass:: ndlib.models.epidemics.ICEModel.ICEModel
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.__init__(graph)
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.set_initial_status(self, configuration)
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.reset(self)
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^^^^^^^^
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Describe
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^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.get_info(self)
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.get_status_map(self)
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^^^^^^^^^^^^^^^^^^
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Execute Simulation
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^^^^^^^^^^^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.iteration(self)
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.. automethod:: ndlib.models.epidemics.ICEModel.ICEModel.iteration_bunch(self, bunch_size)
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-------
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Example
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-------
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In the code below is shown an example of instantiation and execution of an ICE model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population.
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.. code-block:: python
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import networkx as nx
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import ndlib.models.ModelConfig as mc
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import ndlib.models.epidemics as ep
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# Network topology
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g = nx.erdos_renyi_graph(1000, 0.1)
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# Model selection
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model = ep.ICEModel(g)
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# Model Configuration
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config = mc.Configuration()
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config.add_model_parameter('fraction_infected', 0.1)
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model.set_initial_status(config)
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# Simulation execution
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iterations = model.iteration_bunch(200)
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.. [#] L. Milli and G. Rossetti. “Community-Aware Content Diffusion: Embeddednes and Permeability,” in Proceedings of International Conference on Complex Networks and Their Applications, 2019 pp. 362--371.

‎docs/reference/models/epidemics/ICEP.rst

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******************************************************************
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Independent Cascades with Community Embeddedness and Permeability
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******************************************************************
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The Independent Cascades with Community Embeddedness and Permeability model was introduced by Milli and Rossetti in 2020 [#]_.
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This model is a combination of ICE and ICP methods.
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The ICEP model starts with an initial set of **active** nodes A0; the diffusive process unfolds in discrete steps according to the following randomized rule:
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- When node v becomes active in step t, it is given a single chance to activate each currently inactive neighbor u. If v and u belong to the same community, the method acts as the ICE model, otherwise as the ICP model.
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- If u has multiple newly activated neighbors, their attempts are sequenced in an arbitrary order.
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- If v succeeds, then u will become active in step t + 1; but whether or not v succeeds, it cannot make any further attempts to activate u in subsequent rounds.
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- The process runs until no more activations are possible.
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--------
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Statuses
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--------
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During the simulation a node can experience the following statuses:
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=========== ====
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Name Code
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=========== ====
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Susceptible 0
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Infected 1
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Removed 2
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=========== ====
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----------
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Parameters
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----------
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====================== ===== =============== ======= ========= ======================
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Name Type Value Type Default Mandatory Description
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====================== ===== =============== ======= ========= ======================
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Edge threshold Edge float in [0, 1] 0.1 False Edge threshold
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Community permeability Model float in [0, 1] 0.5 True Community Permeability
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====================== ===== =============== ======= ========= ======================
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The initial infection status can be defined via:
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- **fraction_infected**: Model Parameter, float in [0, 1]
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- **Infected**: Status Parameter, set of nodes
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The two options are mutually exclusive and the latter takes precedence over the former.
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-------
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Methods
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-------
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The following class methods are made available to configure, describe and execute the simulation:
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^^^^^^^^^
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Configure
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^^^^^^^^^
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.. autoclass:: ndlib.models.epidemics.ICEPModel.ICEPModel
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.__init__(graph)
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.set_initial_status(self, configuration)
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.reset(self)
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^^^^^^^^
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Describe
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^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.get_info(self)
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.get_status_map(self)
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^^^^^^^^^^^^^^^^^^
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Execute Simulation
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^^^^^^^^^^^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.iteration(self)
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.. automethod:: ndlib.models.epidemics.ICEPModel.ICEPModel.iteration_bunch(self, bunch_size)
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-------
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Example
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-------
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In the code below is shown an example of instantiation and execution of an ICEP model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population, assign a threshold of 0.1 to all the edges and set the community permeability equal 0.3.
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.. code-block:: python
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import networkx as nx
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import ndlib.models.ModelConfig as mc
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import ndlib.models.epidemics as ep
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# Network topology
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g = nx.erdos_renyi_graph(1000, 0.1)
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# Model selection
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model = ep.ICEPModel(g)
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# Model Configuration
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config = mc.Configuration()
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config.add_model_parameter('fraction_infected', 0.1)
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config.add_model_parameter('permeability', 0.3)
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# Setting the edge parameters
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threshold = 0.1
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for e in g.edges():
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config.add_edge_configuration("threshold", e, threshold)
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model.set_initial_status(config)
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# Simulation execution
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iterations = model.iteration_bunch(200)
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.. [#] L. Milli and G. Rossetti. “Barriers or Accelerators? Modeling the two-foldnature of meso-scale network topologies indiffusive phenomena,” 2020

‎docs/reference/models/epidemics/ICP.rst

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**************************************************
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Independent Cascades with Community Permeability
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**************************************************
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The Independent Cascades with Community Permeability model was introduced by Milli and Rossetti in 2019 [#]_.
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This model is a variation of the well-known Independent Cascade (IC), and it is designed to embed community awareness into the IC model.
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This model exploits the idea of permeability. A community is “permeable” to a given content if it permits that content to spread from it fast
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(or vice-versa, if it permits the content to be easily received from nodes outside the community). Conversely, a community has a low degree of permeability if it dampens the diffusion probability across its border.
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The ICP model starts with an initial set of **active** nodes A0; the diffusive process unfolds in discrete steps according to the following randomized rule:
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- When node v becomes active in step t, it is given a single chance to activate each currently inactive neighbor u. If v and u belong to the same community, the method works as a standard IC model (it succeeds with a probability p(v,u)); instead, if the nodes are part of to different communities, the likelihood p(v,u) is dampened of a factor :math:`\eta` (the community permeability parameter).
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- If u has multiple newly activated neighbors, their attempts are sequenced in an arbitrary order.
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- If v succeeds, then u will become active in step t + 1; but whether or not v succeeds, it cannot make any further attempts to activate u in subsequent rounds.
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- The process runs until no more activations are possible.
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--------
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Statuses
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--------
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During the simulation a node can experience the following statuses:
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=========== ====
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Name Code
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=========== ====
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Susceptible 0
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Infected 1
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Removed 2
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=========== ====
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----------
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Parameters
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----------
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====================== ===== =============== ======= ========= ======================
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Name Type Value Type Default Mandatory Description
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====================== ===== =============== ======= ========= ======================
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Edge threshold Edge float in [0, 1] 0.1 False Edge threshold
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Community permeability Model float in [0, 1] 0.5 True Community Permeability
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====================== ===== =============== ======= ========= ======================
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The initial infection status can be defined via:
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- **fraction_infected**: Model Parameter, float in [0, 1]
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- **Infected**: Status Parameter, set of nodes
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The two options are mutually exclusive and the latter takes precedence over the former.
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-------
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Methods
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-------
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The following class methods are made available to configure, describe and execute the simulation:
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^^^^^^^^^
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Configure
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^^^^^^^^^
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.. autoclass:: ndlib.models.epidemics.ICPModel.IndependentCascadesModel
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.__init__(graph)
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.set_initial_status(self, configuration)
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.reset(self)
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^^^^^^^^
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Describe
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^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.get_info(self)
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.get_status_map(self)
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^^^^^^^^^^^^^^^^^^
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Execute Simulation
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^^^^^^^^^^^^^^^^^^
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.iteration(self)
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.. automethod:: ndlib.models.epidemics.ICPModel.ICPModel.iteration_bunch(self, bunch_size)
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-------
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Example
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-------
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In the code below is shown an example of instantiation and execution of an ICP model simulation on a random graph: we set the initial set of infected nodes as 1% of the overall population, assign a threshold of 0.1 to all the edges and set the community permeability equal 0.3.
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.. code-block:: python
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import networkx as nx
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import ndlib.models.ModelConfig as mc
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import ndlib.models.epidemics as ep
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# Network topology
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g = nx.erdos_renyi_graph(1000, 0.1)
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# Model selection
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model = ep.ICPModel(g)
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# Model Configuration
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config = mc.Configuration()
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config.add_model_parameter('fraction_infected', 0.1)
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config.add_model_parameter('permeability', 0.3)
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# Setting the edge parameters
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threshold = 0.1
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for e in g.edges():
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config.add_edge_configuration("threshold", e, threshold)
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model.set_initial_status(config)
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# Simulation execution
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iterations = model.iteration_bunch(200)
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.. [#] L. Milli and G. Rossetti. “Community-Aware Content Diffusion: Embeddednes and Permeability,” in Proceedings of International Conference on Complex Networks and Their Applications, 2019 pp. 362--371.

‎docs/reference/reference.rst

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models/epidemics/Profile.rst
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models/epidemics/ProfileThreshold.rst
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models/epidemics/UTLDR.rst
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models/epidemics/ICEP.rst
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models/epidemics/ICP.rst
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models/epidemics/ICE.rst
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