add Hegselmann-Krause model

docs/reference/models/opinion/ARWHK.rst

@@ -117,8 +117,7 @@ Example
 -------
 
 In the code below is shown an example of instantiation and execution of an ARWHK model simulation on a
-random graph: we set the initial set of infected nodes as 1% of the overall population,
-assign an epsilon value of 0.32, the percentage of stubborness equal 0.2, the distribution of stubborness equal 0
+random graph: we assign an epsilon value of 0.32, the percentage of stubborness equal 0.2, the distribution of stubborness equal 0
 and a weight equal 0.2 to all the edges.
 
 

docs/reference/models/opinion/HK.rst

@@ -0,0 +1,95 @@
+************************************************
+Attraction-Repulsion Weighted Hegselmann-Krause
+************************************************
+
+The Hegselmann-Krause model was introduced in 2002 by Hegselmann, Krause et al [#]_.
+
+During each interaction a random  agenti is  selected  and  the  set :math:`\Gamma_{\epsilon}` of  its  neighbors  whose
+opinions differ at most :math:`\epsilon` (:math:`d_{i,j}=|x_i(t)-x_j(t)|\leq \epsilon`) is identified.
+The selected agent i changes its opinion based on the following update rule:
+
+.. math::
+
+        x_i(t+1)= \frac{\sum_{j \in \Gamma_{\epsilon}} x_j(t)}{\#\Gamma_{\epsilon}}
+
+
+The idea behind the WHK formulation is that the opinion of agent :math:`i` at time :math:`t+1`, will be given by the average
+opinion by its, selected, :math:`\epsilon`-neighbor.
+
+--------
+Statuses
+--------
+
+Node statuses are continuous values in [-1,1].
+
+----------
+Parameters
+----------
+
+===========================  =====  =========================  =======  =========  ==============================================
+Name                         Type   Value Type                 Default  Mandatory  Description
+===========================  =====  =========================  =======  =========  ==============================================
+epsilon                      Model  float in [0, 1]             ---     True       Bounded confidence threshold
+===========================  =====  =========================  =======  =========  ==============================================
+
+-------
+Methods
+-------
+
+The following class methods are made available to configure, describe and execute the simulation:
+
+^^^^^^^^^
+Configure
+^^^^^^^^^
+
+.. autoclass:: ndlib.models.opinions.HKModel.HKModel
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.__init__(graph)
+
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.set_initial_status(self, configuration)
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.reset(self)
+
+^^^^^^^^
+Describe
+^^^^^^^^
+
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.get_info(self)
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.get_status_map(self)
+
+^^^^^^^^^^^^^^^^^^
+Execute Simulation
+^^^^^^^^^^^^^^^^^^
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.iteration(self)
+.. automethod:: ndlib.models.opinions.HKModel.HKModel.iteration_bunch(self, bunch_size)
+
+
+-------
+Example
+-------
+
+In the code below is shown an example of instantiation and execution of an HK model simulation on a random graph:
+we an epsilon value of 0.32 .
+
+
+.. code-block:: python
+
+    import networkx as nx
+    import ndlib.models.ModelConfig as mc
+    import ndlib.models.opinions as opn
+
+    # Network topology
+    g = nx.erdos_renyi_graph(1000, 0.1)
+
+    # Model selection
+    model = opn.HKModel(g)
+
+    # Model Configuration
+    config = mc.Configuration()
+    config.add_model_parameter("epsilon", 0.32)
+
+    model.set_initial_status(config)
+
+    # Simulation execution
+    iterations = model.iteration_bunch(20)
+
+
+.. [#] R. Hegselmann, U. Krause, et al.: “Opinion dynamics and bounded confidence models, analysis, and simulation." in Journal of artificial societies and social simulation, 2002

docs/reference/models/opinion/WHK.rst

@@ -5,16 +5,17 @@ Weighted Hegselmann-Krause
 The Weighted Hegselmann-Krause was introduced by Milli et al. in 2021 [#]_.
 
 This model is a variation of the well-known Hegselmann-Krause (HK).
-Conversely from the HK model, during each iteration WHK consider a random pair-wise interaction involving agents at distance :math:`\epsilon`.
+During each interaction a random  agenti is  selected  and  the  set :math:`\Gamma_{\epsilon}` of  its  neighbors  whose
+opinions differ at most :math:`\epsilon` (:math:`d_{i,j}=|x_i(t)-x_j(t)|\leq \epsilon`) is identified.
 Moreover, to account for the heterogeneity of interaction frequency among agent pairs, WHK leverages edge weights, thus capturing the effect of different social bonds' strength/trust as it happens in reality.
 To such extent, each edge :math:`(i,j) \in E`, carries a value :math:`w_{i,j}\in [0,1]`.
 The update rule then becomes:
 
 .. math::
 
         x_i(t+1)= \left\{ \begin{array}{ll}
-              x_i(t) + \frac{x_i(t) + x_j(t)w_{i,j}}{2} (1-x_i(t)) &  \quad \quad \mbox{if }  x_i(t) \geq 0\\
-              x_i(t) + \frac{x_i(t) + x_j(t)w_{i,j}}{2} (1+x_i(t)) &  \quad \quad \mbox{if } x_i(t) < 0
+               x_i(t) + \frac{\sum_{j \in \Gamma_{\epsilon}} x_j(t)w_{ij}}{\#\Gamma_{\epsilon}} (1-x_i(t)) \quad \quad \text{\quad if   x_i(t) \geq 0}\\
+              x_i(t) + \frac{\sum_{j \in \Gamma_{\epsilon}} x_j(t)w_{ij}}{\#\Gamma_{\epsilon}} (1+x_i(t)) \quad \text{if  x_i(t) < 0 }
                 \end{array}
                 \right.
 
@@ -78,8 +79,7 @@ Example
 -------
 
 In the code below is shown an example of instantiation and execution of an WHK model simulation on a random graph:
-we set the initial set of infected nodes as 1% of the overall population,
-assign an epsilon value of 0.32 and a weight equal 0.2 to all the edges.
+we an epsilon value of 0.32 and a weight equal 0.2 to all the edges.
 
 
 .. code-block:: python

docs/reference/reference.rst

@@ -89,6 +89,7 @@ In ``NDlib`` are implemented the following **Opinion Dynamics** models:
    models/opinion/AlgorithmicBias.rst
    models/opinion/ARWHK.rst
    models/opinion/WHK.rst
+   models/opinion/HK.rst
 
 
 

ndlib/models/opinions/HKModel.py

@@ -0,0 +1,119 @@
+from ndlib.models.DiffusionModel import DiffusionModel
+import future.utils
+import numpy as np
+import random
+from sklearn.metrics import jaccard_score
+
+__author__ = ['Letizia Milli']
+__license__ = "BSD-2-Clause"
+
+class HKModel(DiffusionModel):
+    """
+    Model Parameters to be specified via ModelConfig
+    :param epsilon: bounded confidence threshold from the HK model (float in [0,1])
+    """
+
+    def __init__(self, graph):
+        """
+        Model Constructor
+        :param graph: A networkx graph object
+        """
+        super(self.__class__, self).__init__(graph)
+        self.discrete_state = False
+
+        self.available_statuses = {
+            "Infected": 0
+        }
+
+        self.parameters = {
+            "model": {
+                "epsilon": {
+                    "descr": "Bounded confidence threshold",
+                    "range": [0, 1],
+                    "optional": False,
+                }
+            },
+            "edges": {},
+            "nodes": {},
+        }
+        self.name = "Hegselmann-Krause"
+
+    def set_initial_status(self, configuration=None):
+        """
+        Override behaviour of methods in class DiffusionModel.
+        Overwrites initial status using random real values.
+        """
+        super(HKModel, self).set_initial_status(configuration)
+
+        # set node status
+        for node in self.status:
+            self.status[node] = random.uniform(-1, 1)
+        self.initial_status = self.status.copy()
+
+
+    def clean_initial_status(self, valid_status=None):
+        for n, s in future.utils.iteritems(self.status):
+            if s > 1 or s < -1:
+                self.status[n] = 0.0
+
+    def iteration(self, node_status=True):
+
+        '''
+        Execute a single model iteration
+
+        :return: Iteration_id, Incremental node status (dictionary code -> status)
+        '''
+        # An iteration changes the opinion of the selected agent 'i' .
+
+        self.clean_initial_status(None)
+
+        actual_status = {node: nstatus for node, nstatus in future.utils.iteritems(self.status)}
+
+        if self.actual_iteration == 0:
+            self.actual_iteration += 1
+            delta, node_count, status_delta = self.status_delta(self.status)
+            if node_status:
+                return {"iteration": 0, "status": self.status.copy(),
+                        "node_count": node_count.copy(), "status_delta": status_delta.copy()}
+            else:
+                return {"iteration": 0, "status": {},
+                        "node_count": node_count.copy(), "status_delta": status_delta.copy()}
+
+
+        for i in range(0, self.graph.number_of_nodes()):
+            # select a random node
+            n1 = list(self.graph.nodes)[np.random.randint(0, self.graph.number_of_nodes())]
+
+            # select neighbors of n1
+            neighbours = list(self.graph.neighbors(n1))
+            sum_op = 0
+            count_in_eps = 0
+
+            if len(neighbours) == 0:
+                continue
+
+            for neigh in neighbours:
+                # compute the difference between opinions
+                diff_opinion = np.abs((actual_status[n1]) - (actual_status[neigh]))
+                if diff_opinion < self.params['model']['epsilon']:
+                    sum_op += actual_status[neigh]
+                    # count_in_eps is the number of neighbors in epsilon
+                    count_in_eps += 1
+
+            if (count_in_eps > 0):
+                new_op = sum_op / float(count_in_eps)
+            else:
+                # if there aren't neighbors in epsilon, the status of n1 doesn't change
+                new_op = actual_status[n1]
+
+        actual_status[n1] = new_op
+
+        delta, node_count, status_delta = self.status_delta(actual_status)
+        self.status = actual_status
+        self.actual_iteration += 1
+        if node_status:
+            return {"iteration": self.actual_iteration - 1, "status": delta.copy(), "node_count": node_count.copy(),
+                    "status_delta": status_delta.copy()}
+        else:
+            return {"iteration": self.actual_iteration - 1, "status": {}, "node_count": node_count.copy(),
+                    "status_delta": status_delta.copy()}

ndlib/models/opinions/__init__.py

@@ -14,6 +14,7 @@
 from .VoterModel import VoterModel
 from .WHKModel import WHKModel
 from .ARWHKModel import ARWHKModel
+from .HKModel import HKModel
 
 
 __all__ = [
@@ -25,4 +26,5 @@
     'VoterModel',
     'WHKModel',
     'ARWHKModel',
+    'HKModel'
 ]

ndlib/test/test_ndlib.py

@@ -235,6 +235,19 @@ def test_whk_model(self):
             iterations = model.iteration_bunch(3)
             self.assertEqual(len(iterations), 3)
 
+    def test_hk_model(self):
+        for g in get_graph():
+            model = opn.HKModel(g)
+            config = mc.Configuration()
+            config.add_model_parameter("epsilon", 0.32)
+
+            model.set_initial_status(config)
+
+            iterations = model.iteration_bunch(10)
+            self.assertEqual(len(iterations), 10)
+            iterations = model.iteration_bunch(10, node_status=False)
+            self.assertEqual(len(iterations), 10)
+
     def test_arwhk_model(self):
         for g in get_graph():
             model = opn.ARWHKModel(g)