The Profile model, introduced by Milli et al. in , 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
blockeda node becomes immune to the infection.
- every iteration
adopter_ratepercentage of nodes spontaneous became infected to endogenous effects.
During the simulation a node can experience the following statuses:
|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.
The following class methods are made available to configure, describe and execute the simulation:
- Node Parameters to be specified via ModelConfig
Parameters: profile – The node profile. As default a value of 0.1 is assumed for all nodes.
Parameters: graph – A networkx graph object
Set the initial model configuration
Parameters: configuration – a
Reset the simulation setting the actual status to the initial configuration.
Describes the current model parameters (nodes, edges, status)
Returns: a dictionary containing for each parameter class the values specified during model configuration
Specify the statuses allowed by the model and their numeric code
Returns: a dictionary (status->code)
Execute a single model iteration
Returns: Iteration_id, Incremental node status (dictionary node->status)
NB: the ``execute_iterations()`` method is unavailable for this model (along with other thresholded models).
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()
|||Milli, L., Rossetti, G., Pedreschi, D., & Giannotti, F. (2018). Active and passive diffusion processes in complex networks. Applied network science, 3(1), 42.|