def graph_to_laplacian(G, normalized=True):
"""
Converts a graph from popular Python packages to Laplacian representation.
Currently support NetworkX, graph_tool and igraph.
Parameters
----------
G : obj
Input graph
normalized : bool
Whether to use normalized Laplacian.
Normalized and unnormalized Laplacians capture different properties of graphs, e.g. normalized Laplacian spectrum can determine whether a graph is bipartite, but not the number of its edges. We recommend using normalized Laplacian.
Returns
-------
scipy.sparse
Laplacian matrix of the input graph
Examples
--------
>>> graph_to_laplacian(nx.complete_graph(3), 'unnormalized').todense()
[[ 2, -1, -1], [-1, 2, -1], [-1, -1, 2]]
>>> graph_to_laplacian('test')
None
"""
try:
import networkx as nx
if isinstance(G, nx.Graph):
if normalized:
return nx.normalized_laplacian_matrix(G)
else:
return nx.laplacian_matrix(G)
except ImportError:
pass
try:
import graph_tool.all as gt
if isinstance(G, gt.Graph):
if normalized:
return gt.laplacian_type(G, normalized=True)
else:
return gt.laplacian(G)
except ImportError:
pass
try:
import igraph as ig
if isinstance(G, ig.Graph):
if normalized:
return np.array(G.laplacian(normalized=True))
else:
return np.array(G.laplacian())
except ImportError:
pass
#Figure 1
gt.graph_draw(G,
vertex_text=G.vertex_index,
vertex_font_size=18,
output_size=(800, 800),
output="example2.pdf")
#A will be the adjacency matrix of G
A = gt.adjacency(G)
with open('log.txt', 'w') as file_w:
file_w.write("A_G=\n")
file_w.write(str(A.todense().transpose()))
file_w.write("\n")
L = gt.laplacian(G, deg='total', normalized=False, weight=None,
index=None) # unnormalized Laplace
L = L - A.transpose() #L
with open('log.txt', 'ab') as file_w:
file_w.write("L=\n")
file_w.write(str(L.todense()))
file_w.write("\n")
S, O = numpy.linalg.eigh(L.todense())
with open('log.txt', 'ab') as file_w:
file_w.write("S=\n")
file_w.write(str(S))
file_w.write("\n")
with open('log.txt', 'ab') as file_w: