# Source code for karateclub.node_embedding.neighbourhood.geometriclaplacianeigenmaps

```import numpy as np
import networkx as nx
import scipy.sparse as sps
from karateclub.estimator import Estimator

[docs]class GLEE(Estimator):
r"""An implementation of `"Geometric Laplacian Eigenmaps" <https://arxiv.org/abs/1905.09763>`_
from the Journal of Complex Networks '20 paper "GLEE: Geometric Laplacian Eigenmap Embedding".
The procedure extracts the eigenvectors corresponding to the largest eigenvalues
of the graph Laplacian. These vectors are used as the node embedding.

Args:
dimensions (int): Dimensionality of embedding. Default is 128.
seed (int): Random seed value. Default is 42.
"""

def __init__(self, dimensions: int = 128, seed: int = 42):

self.dimensions = dimensions
self.seed = seed

[docs]    def fit(self, graph: nx.classes.graph.Graph):
"""
Fitting a Geometric Laplacian EigenMaps model.

Arg types:
* **graph** *(NetworkX graph)* - The graph to be embedded.
"""
self._set_seed()
graph = self._check_graph(graph)
number_of_nodes = graph.number_of_nodes()
L_tilde = nx.normalized_laplacian_matrix(graph, nodelist=range(number_of_nodes))
_, self._embedding = sps.linalg.eigsh(
L_tilde, k=self.dimensions + 1, which="LM", return_eigenvectors=True
)

[docs]    def get_embedding(self) -> np.array:
r"""Getting the node embedding.

Return types:
* **embedding** *(Numpy array)* - The embedding of nodes.
"""
return self._embedding
```