Compute.betweenness_centrality()#

relationalai.std.graphs

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

Computes the betweenness centrality of a node. Betweenness centrality measures the importance of a node by counting how often it appears on the shortest paths between pairs of nodes in a graph. Nodes with high betweenness centrality may play critical roles in the flow of information or resources through a network. Must be called in a rule or query context.

Supported Graph Types#

Graph Type	Supported	Notes
Directed	Yes
Undirected	Yes
Weighted	Yes	Weights are ignored.
Unweighted	Yes

Parameters#

Name	Type	Description
node	Producer	A node in the graph.

Algorithm Details#

Calculating betweenness centrality requires determining all shortest paths between each pair of nodes within a graph, which makes it computationally intensive to compute exactly for large networks. betweenness_centrality() gives an approximation using the Brandes-Pich algorithm, which samples nodes uniformly at random and performs single-source shortest-path computations from those nodes.

This implementation nominally samples 100 nodes uniformly at random, yielding time complexity of 100 * O(|V|+|E|) where |V| and |E| are the number of nodes and edges respectively. If the graph has fewer than 100 nodes, the implementation reduces to the exact Brandes algorithm, with time complexity O(|V|(|V|+|E|)) for unweighted graphs.

Returns#

Returns an Expression object that produces the betweenness centrality of the node as a floating-point value.

Example#

Use .betweenness_centrality() to compute the betweenness centrality of a node in a graph. You access the .betweenness_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 betweenness centrality of each person in the graph.
with model.query() as select:
    # Get all person objects.
    person = Person()
    # Compute the betweenness centrality of each person.
    centrality = graph.compute.betweenness_centrality(person)
    # Select the each person's name and their betweenness centrality.
    response = select(person.name, alias(centrality, "betweenness_centrality"))

print(response.results)
# Output:
#     name  betweenness_centrality
# 0  Alice                     2.0
# 1    Bob                     0.0
# 2  Carol                     0.0

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 betweenness 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 betweenness centrality of each object.
    # Objects that are not nodes in the graph are filtered out.
    centrality = graph.compute.betweenness_centrality(obj)
    # Select the each object's name and their betweenness centrality.
    response = select(obj.name, alias(centrality, "betweenness_centrality"))

# Only rows for people are returned, since companies are not nodes in the graph.
print(response.results)
# Output:
#     name  betweenness_centrality
# 0  Alice                     2.0
# 1    Bob                     0.0
# 2  Carol                     0.0