# Node Numerical Attribute¶

Node Numerical Attribute compartments are used to evaluate events attached to numeric edge attributes.

Consider the transition rule Susceptible->Infected that requires a that the susceptible node express a specific value of an internal numeric attribute, attr, to be satisfied (e.g. “Age” == 18). Such rule can be described by a simple compartment that models Node Numerical Attribute selection. Let’s call il NNA.

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

During each rule evaluation, given a node n and one of its neighbors m

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

op represent a logic operator and can assume one of the following values: - equality: “==” - less than: “<” - greater than: “>” - equal or less than: “<=” - equal or greater than: “>=” - not equal to: “!=” - within: “IN”

Moreover, NNA allows to specify a triggering status in order to restrain the compartment evaluation to those nodes that:

1. match the rule initial state, and
2. have at least one neighbors in the triggering status.

## Parameters¶

Name Value Type Default Mandatory Description
attribute string None True Attribute name
value numeric(*) None True Attribute testing value
op string None True Logic operator
probability float in [0, 1] 1 False Event probability
triggering_status string None False Trigger

(*) When op equals “IN” the attribute value is expected to be a tuple of two elements identifying a closed interval.

## Example¶

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

The first compartment, c1, is used to implement the transition rule Susceptible->Infected. It restrain the rule evaluation to all those nodes having “Age” equals to 18.

The second compartment, c2, is used to implement the transition rule Infected->Recovered. It restrain the rule evaluation to all those nodes connected at least to a “Susceptible” neighbor and having “Age” in the range [20, 25].

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

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

# Setting edge attribute
attr = {n: {"Age": random.choice(range(0, 100))} for n in g.nodes()}
nx.set_edge_attributes(g, attr)

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

# Model statuses

# Compartment definition
c1 = na.NodeNumericalAttribute("Age", value=18, op="==", probability=0.6)
c2 = na.NodeNumericalAttribute("Age", value=(20, 25), op="IN", probability=0.6, triggering_status="Susceptible")

# Rule definition