Custom Model Definition

NDlib exposes a set of built-in diffusion models (epidemic/opinion dynamics/dynamic network): how can I describe novel ones?

In order to answer such question we developed a syntax for compositional model definition.

Rationale

At a higher level of abstraction a diffusion process can be synthesized into two components:

  • Available Statuses, and
  • Transition Rules that connect them

All models of NDlib assume an agent-based, discrete time, simulation engine. During each simulation iteration all the nodes in the network are asked to (i) evaluate their current status and to (ii) (eventually) apply a matching transition rule. The last step of such process can be easily decomposed into atomic operations that we will call compartments.

Note

NDlib exposes two classes for defining custom diffusion models:

  • CompositeModel describes diffusion models for static networks
  • DynamicCompositeModel describes diffusion models for dynamic networks

To avoid redundant documentation, here we will discuss only the former class, the latter behaving alike.

Compartments

We adopt the concept of compartment to identify all those atomic conditions (i.e. operations) that describe (part of) a transition rule. The execution of a compartment can return either True (condition satisfied) or False (condition not satisfied).

Indeed, several compartments can be described, each one of them capturing an atomic operation.

To cover the main scenarios we defined three families of compartments as well as some operations to combine them.

Node Compartments

In this class fall all those compartments that evaluate conditions tied to node status/features. They model stochastic events as well as deterministic ones.

Edge Compartments

In this class fall all those compartments that evaluate conditions tied to edge features. They model stochastic events as well as deterministic ones.

Time Compartments

In this class fall all those compartments that evaluate conditions tied to temporal execution. They can be used to model, for instance, lagged events as well as triggered transitions.

Compartments Composition

Compartment can be chained in multiple ways so to describe complex transition rules. In particular, a transition rule can be seen as a tree whose nodes are compartments and edges connections among them.

  • The initial node status is evaluated at the root of the tree (the master compartment)
  • if the operation described by such compartment is satisfied the conditions of (one of) its child compartments is evaluated
  • if a path from the root to one leaf of the tree is completely satisfied the transition rule applies and the node change its status.

Compartments can be combined following two criteria:

A rule can be defined by employing all possible combinations of cascading and conditional compartment composition.

Examples

Here some example of models implemented using compartments.

SIR

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.CompositeModel as gc
import ndlib.models.compartments.NodeStochastic as ns

# Network generation
g = nx.erdos_renyi_graph(1000, 0.1)

# Composite Model instantiation
model = gc.CompositeModel(g)

# Model statuses
model.add_status("Susceptible")
model.add_status("Infected")
model.add_status("Removed")

# Compartment definition
c1 = ns.NodeStochastic(0.02, triggering_status="Infected")
c2 = ns.NodeStochastic(0.01)

# Rule definition
model.add_rule("Susceptible", "Infected", c1)
model.add_rule("Infected", "Removed", c2)

# Model initial status configuration
config = mc.Configuration()
config.add_model_parameter('percentage_infected', 0.1)

# Simulation execution
model.set_initial_status(config)
iterations = model.iteration_bunch(5)