dyvider 0.3

Rapid and exact partitioning algorithms for graphs embedded in one dimension.

dyvider is a small library implementing dynamic programming algorithms for exact linear clustering in networks. Its algorithms process networks whose nodes have positions in one dimension, and return their optimal partition.

The theory and experiments exploring this code can be found in the paper “Exact and rapid linear clustering of networks with dynamic programming”, by Alice Patania, Antoine Allard and Jean-Gabriel Young.

Dependencies

The only necessary dependency are networkx and numpy.

Quick tour

The following minimal example first assigns scores to nodes with a one-dimensional spectral embedding and then retrieves an optimal linear clustering from this embedding using dyvider.

import networkx as nx
import dyvider as dy
import numpy as np

# create a graph
g = nx.stochastic_block_model([10, 10], [[0.5, 0.05], [0.05, 0.5]], seed=42)

# generate a 1-d embedding with the leading eigenvector of the modularity matrix
eigenvals, eigvenvecs = np.linalg.eig(nx.linalg.adjacency_matrix(g).todense())
score = {v: float(eigvenvecs[v, 0]) for v in g.nodes()}

# set the node positions
nx.set_node_attributes(g, score, 'score')

# run dyvider
g = dy.utilities.preprocess(g)
objective_function = dy.objectives.Modularity()
solution, Q = dy.algorithms.run(g, objective_function)

print(solution)

The expected output is:

>>> [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]; [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]]

Our tutorial goes into more detail and demonstrates all the API calls.

Paper

If you use this code, please consider citing:

“Exact and rapid linear clustering of networks with dynamic programming” Alice Patania, Antoine Allard and Jean-Gabriel Young. arXiv:2301.10403.

Author information

Code by Jean-Gabriel Young. Don’t hesitate to get in touch at [e-mail], or via the issues!