add laplacian_spectrum example (#6169)

* add laplacian_spectrum example

* add missing reference to_numpy_array

* Update networkx/linalg/spectrum.py

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

* Update networkx/linalg/spectrum.py

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

* Update networkx/linalg/spectrum.py

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

* Rm unnecessary numpy import.

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

1 files changed, 13 insertions, 1 deletions

diff --git a/networkx/linalg/spectrum.py b/networkx/linalg/spectrum.py
index caa95fc5..66aedbbd 100644
--- a/networkx/linalg/spectrum.py
+++ b/networkx/linalg/spectrum.py
@@ -32,11 +32,23 @@ def laplacian_spectrum(G, weight="weight"):
     Notes
     -----
     For MultiGraph/MultiDiGraph, the edges weights are summed.
-    See to_numpy_array for other options.
+    See :func:`~networkx.convert_matrix.to_numpy_array` for other options.
 
     See Also
     --------
     laplacian_matrix
+
+    Examples
+    --------
+    The multiplicity of 0 as an eigenvalue of the laplacian matrix is equal
+    to the number of connected components of G.
+
+    >>> G = nx.Graph()  # Create a graph with 5 nodes and 3 connected components
+    >>> G.add_nodes_from(range(5))
+    >>> G.add_edges_from([(0, 2), (3, 4)])
+    >>> nx.laplacian_spectrum(G)
+    array([0., 0., 0., 2., 2.])
+
     """
     import scipy as sp
     import scipy.linalg  # call as sp.linalg