Compute#

relationalai.std.graphs

#class relationalai.std.graphs.Compute()

The Compute class serves as a namespace for various graph algorithms. This class is automatically instantiated when you create a Graph object and is accessible via the graph’s .compute attribute. It provides methods for computing basic graph statistics, centrality and similarity measures, community detection, and more.

Methods#

Basic Statistics#

Name	Description	Returns
`.num_edges()`	Get the number of edges in the graph.	`Expression`
`.num_nodes()`	Get the number of nodes in the graph.	`Expression`

Degree#

Name	Description	Returns
`.avg_degree()`	Compute the average degree of the graph.	`Expression`
`.avg_indegree()`	Compute the average indegree of a directed graph. Alias for `.avg_degree()` in undirected graphs.	`Expression`
`.avg_outdegree()`	Compute the average outdegree of a directed graph. Alias for `.avg_degree()` in undirected graphs.	`Expression`
`.degree(node)`	Compute the degree of a node.	`Expression`
`.indegree(node)`	Compute the indegree of a node.	`Expression`
`.max_degree()`	Compute the maximum degree of a graph.	`Expression`
`.max_indegree()`	Compute the maximum indegree a directed graph. Alias for `.max_degree()` in undirected graphs.	`Expression`
`.max_outdegree()`	Compute the maximum outdegree of a directed graph graph. Alias for `.max_degree()` in undirected graphs.	`Expression`
`.min_degree()`	Compute the minimum degree of a graph.	`Expression`
`.min_indegree()`	Compute the minimum indegree of a directed graph. Alias for `.min_degree()` in undirected graphs.	`Expression`
`.min_outdegree()`	Compute the minimum outdegree of a directed graph. Alias for `.min_degree()` in undirected graphs.	`Expression`
`.outdegree(node)`	Compute the outdegree of a node.	`Expression`

Centrality Measures#

Name	Description	Returns
`.betweenness_centrality(node)`	Compute the betweenness centrality of a node.	`Expression`
`.degree_centrality(node)`	Compute the degree centrality of a node.	`Expression`
`.eigenvector_centrality(node)`	Compute the eigenvector centrality of the graph.	`Expression`
`.pagerank(node)`	Compute the PageRank of a node.	`Expression`
`.weighted_degree_centrality(node)`	Compute the weighted degree centrality of a node. Alias for `degree_centrality` in unweighted graphs.	`Expression`

Similarity Measures#

Name	Description	Returns
`.cosine_similarity(node1, node2)`	Compute the cosine similarity between two nodes.	`Expression`
`.jaccard_similarity(node1, node2)`	Compute the Jaccard similarity between two nodes.	`Expression`
`.weighted_cosine_similarity(node1, node2)`	Compute the weighted cosine similarity between two nodes. Alias for `cosine_similarity` in unweighted graphs. Only undirected graphs are supported.	`Expression`
`.weighted_jaccard_similarity(node1, node2)`	Compute the weighted Jaccard similarity between two nodes. Alias for `jaccard_similarity()` in unweighted graphs.	`Expression`

Link Prediction#

Name	Description	Returns
`.adamic_adar(node1, node2)`	Compute the Adamic-Adar index between two nodes.	`Expression`
`.common_neighbor(node1, node2)`	Find the common neighbors between two nodes.	`Expression`
`.preferential_attachment(node1, node2)`	Compute the preferential attachment score between two nodes.	`Expression`

Community Detection#

Name	Description	Returns
`.infomap()`	Assign a community label to each node using the Infomap algorithm.	`Expression`
`.is_triangle(node1, node2, node3)`	Check if three nodes form a triangle.	`Expression`
`.label_propagation(node)`	Assign a community label to `node` using the label propagation algorithm.	`Expression`
`.louvain(node)`	Assign a community label to `node` using the Louvain algorithm.	`Expression`
`.num_triangles()`	Compute the number of triangles in the graph.	`Expression`
`.triangles()`	Find all unique triangles in the graph.	`tuple` of three `Expression` objects.
`.triangle_community(node)`	Assign a community label to `node` using the percolation method.	`Expression`

Clustering#

Name	Description	Returns
`.avg_clustering_coefficient()`	Compute the average clustering coefficient of the graph.	`Expression`
`.local_clustering_coefficient(node)`	Compute the local clustering coefficient of a node.	`Expression`

Connectivity#

Name	Description	Returns
`.is_connected()`	Check if the graph is connected.	`Expression`
`.is_reachable(node1, node2)`	Check if `node2` is reachable from `node1`.	`Expression`
`.reachable_from(node)`	Find all nodes reachable from `node`.	`Expression`
`.weakly_connected_component(node)`	Find the weakly connected component containing `node`.	`Expression`

Distance#

Name	Description	Returns
`.diameter_range()`	Compute lower and upper bounds for the diameter of a graph.	`tuple` of two `Expression` objects.
`.distance(node1, node2)`	Compute the shortest path length between two nodes. Ignores weights in weighted graphs.	`Expression`
`.weighted_distance(node1, node2)`	Compute the shortest path length between two nodes in a weighted graph. Alias for `distance` in unweighted graphs.	`Expression`

Example#

Graph algorithms are executed by calling the appropriate method from a Graph object’s .compute attribute. The following example demonstrates how to compute the PageRank of each person in a social network graph:

#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.
# This graph has three edges: one from Alice to Bob, Alice to Carol, and Carol to Daniel.
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 PageRank of each person.
    pagerank = graph.compute.pagerank(person)
    # Select the each person's name and their PageRank value.
    response = select(person.name, alias(pagerank, "pagerank"))

print(response.results)
# Output:
#      name  pagerank
# 0   Alice  0.324562
# 1     Bob  0.175438
# 2   Carol  0.324562
# 3  Daniel  0.175438

See the documentation for each method in the Methods section for more examples.