Documentation

Build a motif adjacency matrix from an adjacency matrix. Entry (i, j) of a motif adjacency matrix is the sum of the weights of all motifs containing both nodes i and j.

Compute a * (b @ ones) where a, b, ones are square matrices of the same size, and ones contains all entries equal to one. The product * is an entry-wise (Hadamard) product, while @ represents matrix multiplication. This method is more efficient than the naive approach when a or b are sparse.

Compute a .* (ones * b) where a, b, ones are square matrices of the same size, and ones contains all entries equal to one.

Set diagonal entries to zero and sparsify.

Get the indices of the vertices in the largest connected component of a graph from its adjacency matrix.

Get the names of some common motifs as strings.

Build the adjacency matrix G.

Build the double-edge adjacency matrix Gd.

Build the product matrix Gp.

Build the single-edge adjacency matrix Gs.

Build the identity matrix Id.

Build the directed indicator matrix J.

Build the missing-edge indicator matrix J0.

Build the double-edge indicator matrix Jd.

Build the edge-and-diagonal matrix Ie.

Build the vertex-distinct indicator matrix Jn.

Build the single-edge indicator matrix Js.

Build a Laplacian matrix (combinatorial Laplacian or random-walk Laplacian) from a symmetric (weighted) graph adjacency matrix.

Compute the first few eigenvalues by magnitude and associated eigenvectors of a matrix.

Run Laplace embedding on a symmetric (weighted) adjacency matrix with a specified number of eigenvalues and eigenvectors.

Calculate a motif adjacency matrix for a given motif and motif type, optionally restrict it to its largest connected component, and then run Laplace embedding with specified Laplacian type and number of eigenvalues and eigenvectors.

Compute the adjusted Rand index between two clusterings.

Get cluster assignments from a spectrum using k-means++.

Run motif-based spectral clustering on the adjacency matrix of a (weighted directed) network, using a specified motif, motif type, weighting scheme, embedding dimension, number of clusters and Laplacian type. Optionally restrict to the largest connected component before clustering.

Generate a small graph for demonstrations.

Build a sparse matrix of size m, n with non-zero probability p. Edge weights can be unweighted, constant-weighted or Poisson-weighted.

Sample the (weighted) adjacency matrix of a (weighted) bipartite stochastic block model (BSBM).

Sample the (weighted) adjacency matrix of a (weighted) directed stochastic block model (DSBM) with specified parameters.