lapl 0.1.1

Spectral methods: graph Laplacian, eigenmaps, spectral clustering
Documentation

lapl

crates.io Documentation CI

Spectral graph theory primitives for manifold learning and connectivity analysis. Implements graph Laplacians (unnormalized, symmetric, random walk) and spectral embeddings.

Dual-licensed under MIT or Apache-2.0.

crates.io | docs.rs

Quickstart

[dependencies]
lapl = "0.1.0"
ndarray = "0.16"

use lapl::{adjacency_to_laplacian, normalized_laplacian, gaussian_similarity};
use ndarray::array;

// Simple graph: 0 -- 1 -- 2
let adj = array![
    [0.0, 1.0, 0.0],
    [1.0, 0.0, 1.0],
    [0.0, 1.0, 0.0]
];

let lap = adjacency_to_laplacian(&adj);       // L = D - A
let lap_norm = normalized_laplacian(&adj);    // L_sym = I - D^{-1/2} A D^{-1/2}

Functions

Function Purpose
adjacency_to_laplacian Unnormalized L = D - A
normalized_laplacian Symmetric normalized (diagonal=1 for isolated nodes)
normalized_laplacian_checked Rejects graphs with isolated nodes
random_walk_laplacian L_rw = I - D^{-1} A
transition_matrix Random walk P = D^{-1} A
gaussian_similarity RBF kernel similarity
knn_graph k-nearest neighbor graph
epsilon_graph Epsilon-neighborhood
is_connected Check connectivity
laplacian_quadratic_form x^T L x

The Laplacian Zoo

  • Unnormalized L = D - A: Simple but scale-dependent
  • Normalized L_sym: Eigenvalues in [0, 2], used for spectral clustering
  • Random walk L_rw: Same spectrum as L_sym, different eigenvectors