Compute.degree_centrality()#

relationalai.std.graphs

#Compute.degree_centrality(node: Producer) -> Expression

This algorithm computes the degree centrality of a node. For unweighted graphs, it measures the importance of a node based on its degree. Nodes with high degree centrality are well-connected in the graph.

For weighted graphs, the weighted degree centrality of a node is the sum of the weights of the edges incident to the node divided by one less than the number of nodes in the graph.

Must be called in a rule or query context.

Supported Graph Types#

Graph Type	Supported	Notes
Directed	Yes
Undirected	Yes
Weighted	Yes
Unweighted	Yes

Parameters#

Name	Type	Description
node	Producer	A node in the graph.

Returns#

Returns an Expression object that produces the degree centrality of the node as a floating-point value, calculated by the following formula:

#degree centrality = degree of the node / (total number of nodes - 1)

This value is at most 1.0 for simple graphs with no self loops. In graphs with self loops, a node’s degree centrality can exceed 1.0.

Example (Unweighted Graphs)#

Use .degree_centrality() to compute the degree centrality of a node in a graph. You access the .degree_centrality() method from a Graph object’s .compute attribute:

#import relationalai as rai
from relationalai.std import alias
from relationalai.std.graphs import Graph

# Create a model named "socialNetwork" with a Person type.
model = rai.Model("socialNetwork")
Person = model.Type("Person")

# Add some people to the model and connect them with a multi-valued `follows` property.
with model.rule():
    alice = Person.add(name="Alice")
    bob = Person.add(name="Bob")
    carol = Person.add(name="Carol")
    alice.follows.extend([bob, carol])
    bob.follows.add(alice)
    carol.follows.add(alice)

# Create a directed graph with Person nodes and edge from people to the people they follow.
# Note that graphs are directed by default.
graph = Graph(model)
graph.Node.extend(Person)
graph.Edge.extend(Person.follows)

# Compute the degree centrality of each person in the graph.
with model.query() as select:
    # Get all person objects.
    person = Person()
    # Compute the degree centrality of each person.
    centrality = graph.compute.degree_centrality(person)
    # Select the each person's name and their degree centrality.
    response = select(person.name, alias(centrality, "degree_centrality"))

print(response.results)
# Output:
#     name  degree_centrality
# 0  Alice                2.0
# 1    Bob                1.0
# 2  Carol                1.0

If one of the objects produced by the node producer is not a node in the graph, no exception is raised. Instead, that object is filtered from the rule or query:

## Add a Company type to the model.
Company = model.Type("Company")

# Add some companies to the model.
with model.rule():
    apple = Company.add(name="Apple")
    google = Company.add(name="Google")

# Get the degree centrality of each person and company in the graph.
with model.query() as select:
    # Get all person and company objects.
    obj = (Person | Company)()
    # Compute the degree centrality of each object.
    # Objects that are not nodes in the graph are filtered out.
    centrality = graph.compute.degree_centrality(obj)
    # Select the each object's name and their degree centrality.
    response = select(obj.name, alias(centrality, "degree_centrality"))

# Only rows for people are returned, since companies are not nodes in the graph.
print(response.results)
# Output:
#     name  degree_centrality
# 0  Alice                2.0
# 1    Bob                1.0
# 2  Carol                1.0

Example (Weighted Graphs)#

Use .degree_centrality() to compute the weighted degree centrality of a node in a graph. You access the .degree_centrality() method from a Graph object’s .compute attribute:

#import relationalai as rai
from relationalai.std import alias
from relationalai.std.graphs import Graph

# Create a model named "socialNetwork" with Person and Friendship types.
model = rai.Model("socialNetwork")
Person = model.Type("Person")
Friendship = model.Type("Friendship")

# Add some people to the model and connect them with friendships.
with model.rule():
    alice = Person.add(name="Alice")
    bob = Person.add(name="Bob")
    carol = Person.add(name="Carol")
    Friendship.add(person1=alice, person2=bob, strength=100)
    Friendship.add(person1=bob, person2=carol, strength=10)

# Create an weighted, undirected graph with Person nodes and edges between friends.
# This graph has two edges: one from Alice and Bob and one from Bob and Carol.
# The edges are weighted by the strength of each friendship.
graph = Graph(model, undirected=True, weighted=True)
graph.Node.extend(Person)
with model.rule():
    friendship = Friendship()
    graph.Edge.add(friendship.person1, friendship.person2, weight=friendship.strength)

# Compute the weighted degree centrality of each person in the graph.
with model.query() as select:
    person = Person()
    centrality = graph.compute.degree_centrality(person)
    response = select(person.name, alias(centrality, "degree_centrality"))

print(response.results)
# Output:
#     name  degree_centrality
# 0  Alice                        50.0
# 1    Bob                        55.0
# 2  Carol                         5.0