Compute.eigenvector_centrality()#

relationalai.std.graphs
#Compute.eigenvector_centrality(node: Producer) -> Expression

Computes the eigenvector centrality of a node in an undirected graph. Eigenvector centrality measures a node’s significance in a graph, taking into account not only its direct connections, but also the centrality of those connected nodes. Specifically, it assigns to each node a centrality score that is proportional to the sum of the centrality scores of its neighboring nodes. Thus, nodes with high eigenvector centrality are important because they are connected to other important nodes. Must be called in a rule or query context.

Directed graphs are not currently supported. See .pagerank() for a similar measure that works with directed graphs.

Supported Graph Types#

Graph TypeSupportedNotes
DirectedNoCurrently not supported.
UndirectedYesSee Returns for convergence criteria.
WeightedYesWeights must be non-negative.
UnweightedYesEdge weights default to 1.0.

Parameters#

NameTypeDescription
nodeProducerA node in the graph.

Returns#

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

We use the power iteration method, which converges if the absolute values of the top two eigenvalues of the adjacency matrix are distinct.

Example#

Use .eigenvector_centrality() to compute the eigenvector centrality of a node in an undirected graph. Directed graphs are currently not supported.

You access the .eigenvector_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 'friends' property.
with model.rule():
    alice = Person.add(name="Alice")
    bob = Person.add(name="Bob")
    carol = Person.add(name="Carol")
    daniel = Person.add(name="Daniel")
    alice.friends.extend([bob, carol])
    carol.friends.add(daniel)

# Create an undirected graph with Person nodes and edges from people to their friends.
graph = Graph(model, undirected=True)
graph.Node.extend(Person)
graph.Edge.extend(Person.friends)

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

print(response.results)
# Output:
#      name  eigenvector_centrality
# 0   Alice                0.601501
# 1     Bob                0.371748
# 2   Carol                0.601501
# 3  Daniel                0.371748

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")

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

# Only rows for people are returned, since companies are not nodes in the graph.
print(response.results)
# Output:
#      name  eigenvector_centrality
# 0   Alice                0.601501
# 1     Bob                0.371748
# 2   Carol                0.601501
# 3  Daniel                0.371748

See Also#