Describe a Diffusion Model

All the diffusion models implemented in NDlib extends the abstract class ndlib.models.DiffusionModel.

class ndlib.models.DiffusionModel.DiffusionModel(graph)

Partial Abstract Class that defines Diffusion Models

Such class implements the logic behind model construction, configuration and execution.

In order to describe a novel diffusion algorithm the following steps must be followed:

Model Description

As convention a new model should be described in a python file named after it, e.g. a MyModule class should be implemented in a MyModule.py file.

DiffusionModel.__init__(self, graph)

Model Constructor

Parameters:graph – A networkx graph object

In oder to effectively describe the model the __init__ function of ndlib.models.DiffusionModel must be specified as follows:

from ndlib.models.DiffusionModel import DiffusionModel

class MyModel(DiffusionModel):

        def __init__(self, graph):

                # Call the super class constructor
                super(self.__class__, self).__init__(graph)

                # Method name
                self.name = "MyModel"

                # Available node statuses
                self.available_statuses = {
                        "Status_0": 0,
                        "Status_1": 1
                }
                # Exposed Parameters
                self.parameters = {
                        "model":
                                "parameter_name": {
                                        "descr": "Description 1"
                                        "range": [0,1],
                                        "optional": False
                                        },
                                },
                        "nodes":
                                "node_parameter_name": {
                                        "descr": "Description 2"
                                        "range": [0,1],
                                        "optional": True
                                        },
                                },
                        "edges":
                                "edge_parameter_name": {
                                                "descr": "Description 3"
                                                "range": [0,1],
                                                "optional": False
                                        },
                                },
                        }

In the __init__ methods three components are used to completely specify the model:

  • self.name: its name;
  • self.available_statuses: the node statuses it allows along with an associated numerical code;
  • self.parameters: the parameters it requires, their range, description and optionality.

All those information will be used to check the user provided configurations as well as metadata for visualizations.

Iteration Rule

Once described the model metadata it is necessary to provide the agent-based description of its general iteration-step.

DiffusionModel.iteration(self)

Execute a single model iteration

Parameters:node_status – if the incremental node status has to be returned.
Returns:Iteration_id, (optional) Incremental node status (dictionary node->status), Status count (dictionary status->node count), Status delta (dictionary status->node delta)

To do so, the iteration() method of the base class has to be overridden in MyModel as follows:

def iteration(self, node_status=True):

        self.clean_initial_status(self.available_statuses.values())

        # if first iteration return the initial node status
        if self.actual_iteration == 0:
                self.actual_iteration += 1
                delta, node_count, status_delta = self.status_delta(actual_status)
                if node_status:
                        return {"iteration": 0, "status": actual_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()}

        actual_status = {node: nstatus for node, nstatus in self.status.iteritems()}

        # iteration inner loop
        for u in self.graph.nodes():
                # evluate possible status changes using the model parameters (accessible via self.params)
                # e.g. self.params['beta'], self.param['nodes']['threshold'][u], self.params['edges'][(id_node0, idnode1)]

        # identify the changes w.r.t. previous iteration
        delta, node_count, status_delta = self.status_delta(actual_status)

        # update the actual status and iterative step
        self.status = actual_status
        self.actual_iteration += 1

        # return the actual configuration (only nodes with status updates)
        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()}

The provided template is composed by 4 steps:

  1. first iteration handling: if present the model returns as result of the first iteration is initial status;
  2. making a copy of the actual diffusion status;
  3. iteration loop: definition, and application, of the rules that regulates individual node status transitions;
  4. construction of the incremental result.

All the steps are mandatory in order to assure a consistent behaviour across different models

All the user specified parameters (models as well as nodes and edges ones) can be used within the iteration() method: to access them an internal data structure is provided, self.params.

self.params is a dictionary that collects all the passed values using the following notation:

  • Model parameters: self.params['model']['parameter_name']
  • Node parameters: self.param['nodes']['nodes_parameter'][node_id]
  • Edge parameters: self.param['edges']['edges_parameter'][(node_id1, node_id2)]

Within the iteration loop the node status updates must be made on the actual_status data structure, e.g. the copy made during Step 1.

Each iteration returns the incremental status of the diffusion process as well as the iteration progressive number.