# Edge Categorical Attribute¶

Edge Categorical Attribute compartments are used to evaluate events attached to edge attributes.

Consider the transition rule Susceptible->Infected that requires a that the susceptible node is connected to a neighbor through a link expressing a specific value of an internal attribute, attr, to be satisfied (e.g. “type”=”co-worker”). Such rule can be described by a simple compartment that models Edge Categorical Attribute selection. Let’s call il ECA.

The rule will take as input the initial node status (Susceptible), the final one (Infected) and the ECA compartment. ECA 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,m) == attr
• a random value b in [0,1] will be generated
• if b <= beta, then ECA is considered satisfied and the status of n changes from initial to final.

Moreover, ECA 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 string None True Attribute testing value
probability float in [0, 1] 1 False Event probability
triggering_status string None False Trigger

## Example¶

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

The first compartment, c1, is used to implement the transition rule Susceptible->Infected. It restrain the rule evaluation to all those nodes connected through a link having the attribute “type” equals “co-worker”.

The second compartment, c2, is used to implement the transition rule Infected->Recovered. It restrain the rule evaluation to all those nodes connected trough a link having the attribute “type” equals “family” whose neighbors is “Susceptible”.

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

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

# Setting edge attribute
attr = {e: {"type": random.choice(['co-worker', 'family'])} for e in g.edges()}
nx.set_edge_attributes(g, attr)

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

# Model statuses

# Compartment definition
c1 = na.NodeCategoricalAttribute("type", "co-worker", probability=0.6)
c2 = na.NodeCategoricalAttribute("type", "family", probability=0.6, triggering_status="Susceptible")

# Rule definition