# Node Numerical Variable¶

Node Numerical Variable compartments are used to evaluate events attached to numeric edge attributes or statuses.

Consider the transition rule Addicted->Not addicted that requires that the susceptible node satisfies a specific condition of an internal numeric attribute, attr, to be satisfied (e.g. “Self control” attr < “Craving” status). Such a rule can be described by a simple compartment that models Node Numerical Attribute and Status selection. Let’s call it NNV.

The rule will take as input the initial node status (Susceptible), the final one (Infected) and the NNV compartment. NNV 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 var(n) op var(n) (where var(n) = attr(n) or status(n))
• a random value b in [0,1] will be generated
• if b <= beta, then NNV 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, NNV 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.

The type of the values that are compared have to be specified in advance, which is done using an enumerated type. This is done to specify whether the first value to be compared is either a status or an attribute, the same thing is done for the second value to be compared. If the value type is not specified, the value to compare the variable to should be a number.

## Parameters¶

Name Value Type Default Mandatory Description
variable string None True The name of the variable to compare
variable_type NumericalType None True Numerical type enumerated value
value numeric(*)|string None True Name of the testing value or number
value_type NumericalType None False Numerical type enumerated 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 the formulation of a model is shown using NodeNumericalVariable compartments.

The first compartment, condition, is used to implement the transition rule Susceptible->Infected. It restrains the rule evaluation to all those nodes having more “Friends” than 18.

The second compartment, condition2, is used to implement the transition rule Infected->Recovered. It restrains the rule evaluation to all those nodes where “Age” is less than the amount of “Friends” attributes.

Note that instead of attributes, the states could have been used as well by using NumericalType.STATUS instead. This would only be applicable for numerical states, which can be modelled when using the ContinuousModel instead of the CompositeModel.

import networkx as nx
import random
import numpy as np

from ndlib.models.CompositeModel import CompositeModel
from ndlib.models.compartments.NodeStochastic import NodeStochastic
from ndlib.models.compartments.enums.NumericalType import NumericalType
from ndlib.models.compartments.NodeNumericalVariable import NodeNumericalVariable
import ndlib.models.ModelConfig as mc

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

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

# Composite Model instantiation
model = CompositeModel(g)

# Model statuses

# Compartment definition
condition = NodeNumericalVariable('Friends', var_type=NumericalType.ATTRIBUTE, value=18, op='>')
condition2 = NodeNumericalVariable('Age', var_type=NumericalType.ATTRIBUTE, value='Friends', value_type=NumericalType.ATTRIBUTE, op='<')

# Rule definition