# Node Categorical Attribute¶

Node Categorical Attribute compartments are used to evaluate events attached to network nodes attributes.

Consider the transition rule Susceptible->Infected that requires a that the susceptible node express a specific value of an internal attribute, attr, to be satisfied (e.g. “Sex”=”male”). Such rule can be described by a simple compartment that models Node Categorical Attribute selection. Let’s call il NCA.

The rule will take as input the initial node status (Susceptible), the final one (Infected) and the NCA compartment. NCA will thus require a probability (beta) of activation.

During each rule evaluation, given a node n

• if the actual status of n equals the rule initial one
• a random value b in [0,1] will be generated
• if b <= beta and attr(n) == attr, then NCA is considered satisfied and the status of n changes from initial to final.

## Parameters¶

Name Value Type Default Mandatory Description
attribute string None True Attribute name
value string None True Attribute testing value
probability float in [0, 1] 1 False Event probability

## Example¶

In the code below is shown the formulation of a model using NodeCategoricalAttribute compartments.

The compartment, c1, is used to implement the transition rule Susceptible->Infected. It restrain the rule evaluation to all those nodes for which the attribute “Sex” equals “male”.

import networkx as nx
import random
import ndlib.models.ModelConfig as mc
import ndlib.models.CompositeModel as gc
import ndlib.models.compartments as cpm

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

# Setting node attribute
attr = {n: {"Sex": random.choice(['male', 'female'])} for n in g.nodes()}
nx.set_node_attributes(g, attr)

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

# Model statuses

# Compartment definition
c1 = cpm.NodeCategoricalAttribute("Sex", "male", probability=0.6)

# Rule definition