Profile¶

The Profile model, introduced by Milli et al. in [1], assumes that the diffusion process is only apparent; each node decides to adopt or not a given behavior – once known its existence – only on the basis of its own interests.

In this scenario the peer pressure is completely ruled out from the overall model: it is not important how many of its neighbors have adopted a specific behaviour, if the node does not like it, it will not change its interests.

Each node has its own profile describing how many it is likely to accept a behaviour similar to the one that is currently spreading.

The diffusion process starts from a set of nodes that have already adopted a given behaviour S:

for each of the susceptible nodes’ in the neighborhood of a node u in S an unbalanced coin is flipped, the unbalance given by the personal profile of the susceptible node;
if a positive result is obtained the susceptible node will adopt the behaviour, thus becoming infected.
if the blocked status is enabled, after having rejected the adoption with probability blocked a node becomes immune to the infection.
every iteration adopter_rate percentage of nodes spontaneous became infected to endogenous effects.

Statuses¶

During the simulation a node can experience the following statuses:

Name	Code
Susceptible	0
Infected	1
Blocked	-1

Parameters¶

Name	Type	Value Type	Default	Mandatory	Description
profile	Node	float in [0, 1]	0.1	False	Node profile
blocked	Model	float in [0, 1]	0	False	Blocked nodes
adopter_rate	Model	float in [0, 1]	0	False	Autonomous adoption

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.

NB: the ``execute_iterations()`` method is unavailable for this model (along with other thresholded models).

Example¶

In the code below is shown an example of instantiation and execution of a Profile model simulation on a random graph: we set the initial infected node set to the 10% of the overall population and assign a profile of 0.25 to all the nodes.

import networkx as nx
import dynetx as dn
import ndlib.models.ModelConfig as mc
import ndlib.models.dynamic as dm
from past.builtins import xrange

# Dynamic Network topology
dg = dn.DynGraph()

for t in xrange(0, 3):
    g = nx.erdos_renyi_graph(200, 0.05)
    dg.add_interactions_from(g.edges(), t)

# Model selection
model = dm.DynProfileModel(dg)
config = mc.Configuration()
config.add_model_parameter('blocked', 0)
config.add_model_parameter('adopter_rate', 0)
config.add_model_parameter('fraction_infected', 0.1)

# Setting nodes parameters
profile = 0.15
for i in g.nodes():
    config.add_node_configuration("profile", i, profile)

model.set_initial_status(config)


# Simulate snapshot based execution
iterations = model.execute_snapshots()