GraphBLAS Algorithms

GraphBLAS algorithms written in Python with Python-graphblas. We are trying to target the NetworkX API algorithms where possible.

Installation

conda install -c conda-forge graphblas-algorithms

pip install graphblas-algorithms

Basic Usage

First, create a GraphBLAS Matrix.

import graphblas as gb

M = gb.Matrix.from_coo(
  [0, 0, 1, 2, 2, 3],
  [1, 3, 0, 0, 1, 2],
  [1., 2., 3., 4., 5., 6.],
  nrows=4, ncols=4, dtype='float32'
)

Next wrap the Matrix as ga.Graph.

import graphblas_algorithms as ga

G = ga.Graph(M)

Finally call an algorithm.

hubs, authorities = ga.hits(G)

When the result is a value per node, a gb.Vector will be returned. In the case of HITS, two Vectors are returned representing the hubs and authorities values.

Algorithms whose result is a subgraph will return ga.Graph.

Plugin for NetworkX

Dispatching to plugins is a new feature in Networkx 3.0. When both networkx and graphblas-algorithms are installed in an environment, calls to NetworkX algorithms can be dispatched to the equivalent version in graphblas-algorithms.

Dispatch Example

import networkx as nx
import graphblas_algorithms as ga

# Generate a random graph (5000 nodes, 1_000_000 edges)
G = nx.erdos_renyi_graph(5000, 0.08)

# Explicitly convert to ga.Graph
G2 = ga.Graph.from_networkx(G)

# Pass G2 to NetworkX's k_truss
T5 = nx.k_truss(G2, 5)

G2 is not a nx.Graph, but it does have an attribute __networkx_plugin__ = "graphblas". This tells NetworkX to dispatch the k_truss call to graphblas-algorithms. This link connection exists because graphblas-algorithms registers itself as a "networkx.plugin" entry point.

The result T5 is a ga.Graph representing the 5-truss structure of the original graph. To convert to a NetworkX Graph, use:

T5.to_networkx()

Note that even with the conversions to and from ga.Graph, this example still runs 10x faster than using the native NetworkX k-truss implementation. Speed improvements scale with graph size, so larger graphs will see an even larger speed-up relative to NetworkX.

Plugin Algorithms

The following NetworkX algorithms have been implemented by graphblas-algorithms and can be used following the dispatch pattern shown above.

• Boundary
  • edge_boundary
  • node_boundary
• Centrality
  • degree_centrality
  • eigenvector_centrality
  • in_degree_centrality
  • katz_centrality
  • out_degree_centrality
• Cluster
  • average_clustering
  • clustering
  • generalized_degree
  • square_clustering
  • transitivity
  • triangles
• Community
  • inter_community_edges
  • intra_community_edges
• Core
  • k_truss
• Cuts
  • boundary_expansion
  • conductance
  • cut_size
  • edge_expansion
  • mixing_expansion
  • node_expansion
  • normalized_cut_size
  • volume
• DAG
  • ancestors
  • descendants
• Dominating
  • is_dominating_set
• Isolate
  • is_isolate
  • isolates
  • number_of_isolates
• Link Analysis
  • hits
  • pagerank
• Reciprocity
  • overall_reciprocity
  • reciprocity
• Regular
  • is_k_regular
  • is_regular
• Shortest Paths
  • floyd_warshall
  • floyd_warshall_predecessor_and_distance
  • single_source_bellman_ford_path_length
  • all_pairs_bellman_ford_path_length
  • has_path
• Simple Paths
  • is_simple_path
• S Metric
  • s_metric
• Structural Holes
  • mutual_weight
• Tournament
  • is_tournament
  • score_sequence
  • tournament_matrix
• Triads
  • is_triad