lapl 0.2.0

Spectral methods: graph Laplacian, eigenmaps, spectral clustering
Documentation

lapl

crates.io Documentation CI

Spectral graph methods.

Dual-licensed under MIT or Apache-2.0.

crates.io | docs.rs

See examples/README.md for the runnable spectral diagnostic example.

Quickstart

[dependencies]
lapl = "0.2"
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
symmetric_eigenvalues Eigenvalues for symmetric matrices

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