def test_weight_keyword(self):
WP4 = nx.Graph()
WP4.add_edges_from( (n,n+1,dict(weight=0.5,other=0.3)) for n in range(3) )
P4 = path_graph(4)
A = nx.to_numpy_array(P4)
np_assert_equal(A, nx.to_numpy_array(WP4,weight=None))
np_assert_equal(0.5*A, nx.to_numpy_array(WP4))
np_assert_equal(0.3*A, nx.to_numpy_array(WP4,weight='other'))
def test_numpy_multigraph(self):
G=nx.MultiGraph()
G.add_edge(1,2,weight=7)
G.add_edge(1,2,weight=70)
A=nx.to_numpy_array(G)
assert_equal(A[1,0],77)
A=nx.to_numpy_array(G,multigraph_weight=min)
assert_equal(A[1,0],7)
A=nx.to_numpy_array(G,multigraph_weight=max)
assert_equal(A[1,0],70)
def test_tnet_to_nx():
df = pd.DataFrame({'i': [0, 0], 'j': [1, 2], 't': [0, 1]})
dfnx = teneto.utils.tnet_to_nx(df, t=0)
G = nx.to_numpy_array(dfnx)
if not G.shape == (2, 2):
raise AssertionError()
if not G[0, 1] == 1:
raise AssertionError()
def test_dtype_int_multigraph(self):
"""Test that setting dtype int actually gives an integer array.
For more information, see GitHub pull request #1363.
"""
G = nx.MultiGraph(nx.complete_graph(3))
A = nx.to_numpy_array(G, dtype=int)
assert_equal(A.dtype, int)
def test_nodelist(self):
"""Conversion from graph to array to graph with nodelist."""
P4 = path_graph(4)
P3 = path_graph(3)
nodelist = list(P3)
A = nx.to_numpy_array(P4, nodelist=nodelist)
GA = nx.Graph(A)
self.assert_equal(GA, P3)
# Make nodelist ambiguous by containing duplicates.
nodelist += [nodelist[0]]
assert_raises(nx.NetworkXError, nx.to_numpy_array, P3, nodelist=nodelist)
def spectral_layout(G, weight='weight', scale=1, center=None, dim=2):
"""Position nodes using the eigenvectors of the graph Laplacian.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spectral_layout(G)
Notes
-----
Directed graphs will be considered as undirected graphs when
positioning the nodes.
For larger graphs (>500 nodes) this will use the SciPy sparse
eigenvalue solver (ARPACK).
"""
# handle some special cases that break the eigensolvers
import numpy as np
G, center = _process_params(G, center, dim)
if len(G) <= 2:
if len(G) == 0:
pos = np.array([])
elif len(G) == 1:
pos = np.array([center])
else:
pos = np.array([np.zeros(dim), np.array(center) * 2.0])
return dict(zip(G, pos))
try:
# Sparse matrix
if len(G) < 500: # dense solver is faster for small graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype='d')
# Symmetrize directed graphs
if G.is_directed():
A = A + np.transpose(A)
pos = _sparse_spectral(A, dim)
except (ImportError, ValueError):
# Dense matrix
A = nx.to_numpy_array(G, weight=weight)
# Symmetrize directed graphs
if G.is_directed():
A += A.T
pos = _spectral(A, dim)
pos = rescale_layout(pos, scale) + center
pos = dict(zip(G, pos))
return pos
def test_identity_digraph_array(self):
"""Conversion from digraph to array to digraph."""
A = nx.to_numpy_array(self.G2)
self.identity_conversion(self.G2, A, nx.DiGraph())
def google_matrix(
G, alpha=0.85, personalization=None, nodelist=None, weight="weight", dangling=None
):
"""Returns the Google matrix of the graph.
Parameters
----------
G : graph
A NetworkX graph. Undirected graphs will be converted to a directed
graph with two directed edges for each undirected edge.
alpha : float
The damping factor.
personalization: dict, optional
The "personalization vector" consisting of a dictionary with a
key some subset of graph nodes and personalization value each of those.
At least one personalization value must be non-zero.
If not specfiied, a nodes personalization value will be zero.
By default, a uniform distribution is used.
nodelist : list, optional
The rows and columns are ordered according to the nodes in nodelist.
If nodelist is None, then the ordering is produced by G.nodes().
weight : key, optional
Edge data key to use as weight. If None weights are set to 1.
dangling: dict, optional
The outedges to be assigned to any "dangling" nodes, i.e., nodes without
any outedges. The dict key is the node the outedge points to and the dict
value is the weight of that outedge. By default, dangling nodes are given
outedges according to the personalization vector (uniform if not
specified) This must be selected to result in an irreducible transition
matrix (see notes below). It may be common to have the dangling dict to
be the same as the personalization dict.
Returns
-------
A : NumPy matrix
Google matrix of the graph
Notes
-----
The matrix returned represents the transition matrix that describes the
Markov chain used in PageRank. For PageRank to converge to a unique
solution (i.e., a unique stationary distribution in a Markov chain), the
transition matrix must be irreducible. In other words, it must be that
there exists a path between every pair of nodes in the graph, or else there
is the potential of "rank sinks."
This implementation works with Multi(Di)Graphs. For multigraphs the
weight between two nodes is set to be the sum of all edge weights
between those nodes.
See Also
--------
pagerank, pagerank_numpy, pagerank_scipy
"""
import numpy as np
# TODO: Remove this warning in version 3.0
import warnings
warnings.warn(
"google_matrix will return an np.ndarray instead of a np.matrix in\n"
"NetworkX version 3.0.",
FutureWarning,
stacklevel=2,
)
if nodelist is None:
nodelist = list(G)
A = nx.to_numpy_array(G, nodelist=nodelist, weight=weight)
N = len(G)
if N == 0:
# TODO: Remove np.asmatrix wrapper in version 3.0
return np.asmatrix(A)
# Personalization vector
if personalization is None:
p = np.repeat(1.0 / N, N)
else:
p = np.array([personalization.get(n, 0) for n in nodelist], dtype=float)
if p.sum() == 0:
raise ZeroDivisionError
p /= p.sum()
# Dangling nodes
if dangling is None:
dangling_weights = p
else:
# Convert the dangling dictionary into an array in nodelist order
dangling_weights = np.array([dangling.get(n, 0) for n in nodelist], dtype=float)
dangling_weights /= dangling_weights.sum()
dangling_nodes = np.where(A.sum(axis=1) == 0)[0]
# Assign dangling_weights to any dangling nodes (nodes with no out links)
A[dangling_nodes] = dangling_weights
A /= A.sum(axis=1)[:, np.newaxis] # Normalize rows to sum to 1
# TODO: Remove np.asmatrix wrapper in version 3.0
return np.asmatrix(alpha * A + (1 - alpha) * p)
def spectral_layout(G, weight="weight", scale=1, center=None, dim=2):
"""Position nodes using the eigenvectors of the graph Laplacian.
Using the unnormalized Laplacian, the layout shows possible clusters of
nodes which are an approximation of the ratio cut. If dim is the number of
dimensions then the positions are the entries of the dim eigenvectors
corresponding to the ascending eigenvalues starting from the second one.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spectral_layout(G)
Notes
-----
Directed graphs will be considered as undirected graphs when
positioning the nodes.
For larger graphs (>500 nodes) this will use the SciPy sparse
eigenvalue solver (ARPACK).
"""
# handle some special cases that break the eigensolvers
import numpy as np
G, center = _process_params(G, center, dim)
if len(G) <= 2:
if len(G) == 0:
pos = np.array([])
elif len(G) == 1:
pos = np.array([center])
else:
pos = np.array([np.zeros(dim), np.array(center) * 2.0])
return dict(zip(G, pos))
try:
# Sparse matrix
if len(G) < 500: # dense solver is faster for small graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype="d")
# Symmetrize directed graphs
if G.is_directed():
A = A + np.transpose(A)
pos = _sparse_spectral(A, dim)
except (ImportError, ValueError):
# Dense matrix
A = nx.to_numpy_array(G, weight=weight)
# Symmetrize directed graphs
if G.is_directed():
A += A.T
pos = _spectral(A, dim)
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
def save_graph(path_output, graph):
format = '%1.4f'
matrix = nx.to_numpy_array(graph)
np.savetxt(path_output, matrix, delimiter=',', fmt=format)
return matrix
#diff = np.array(diff.tolist()).reshape(-1, max_nodes, max_nodes)
#feat = np.array(feat.tolist()).reshape(-1, max_nodes, feat_dim)
#import pdb; pdb.set_trace()
return adj, diff, feat, labels, num_nodes
if __name__ == '__main__':
# MUTAG, PTC_M R, IMDB-BINARY, IMDB-MULTI, REDDIT-BINARY, REDDIT-MULTI-5K,
# adj, diff, feat, labels = load('REDDIT-BINARY')
dataset = 'REDDIT-BINARY'
basedir = os.path.dirname(os.path.abspath(__file__))
datadir = os.path.join(basedir, 'data', dataset)
graphs, diff = process(dataset)
feat, adj, labels = [], [], []
for idx, graph in enumerate(graphs):
adj.append(nx.to_numpy_array(graph))
labels.append(graph.graph['label'])
feat.append(
np.array(list(nx.get_node_attributes(graph, 'feat').values())))
adj, diff, feat, labels = np.array(adj), np.array(diff), np.array(
feat), np.array(labels)
np.save(f'{datadir}/adj.npy', adj)
#np.save(f'{datadir}/diff.npy', diff)
np.save(f'{datadir}/feat.npy', feat)
np.save(f'{datadir}/labels.npy', labels)
# import pdb; pdb.set_trace()
print('done')
def test_identity_weighted_graph_array(self):
"""Conversion from weighted graph to array to weighted graph."""
A = nx.to_numpy_array(self.G3)
self.identity_conversion(self.G3, A, nx.Graph())
def hub_matrix(G, nodelist=None):
"""Returns the HITS hub matrix."""
M = nx.to_numpy_array(G, nodelist=nodelist)
return M @ M.T
def test_identity_graph_array(self):
"Conversion from graph to array to graph."
A = nx.to_numpy_array(self.G1)
self.identity_conversion(self.G1, A, nx.Graph())
def test_identity_digraph_array(self):
"""Conversion from digraph to array to digraph."""
A = nx.to_numpy_array(self.G2)
self.identity_conversion(self.G2, A, nx.DiGraph())
def get_edge_index(self):
adj = torch.Tensor(nx.to_numpy_array(self))
edge_index, _ = dense_to_sparse(adj)
return edge_index
def test_adjacency_interface_numpy(self):
A = nx.to_numpy_array(self.Gs)
pos = nx.drawing.layout._fruchterman_reingold(A)
assert_equal(pos.shape, (6, 2))
pos = nx.drawing.layout._fruchterman_reingold(A, dim=3)
assert_equal(pos.shape, (6, 3))
def plot_connectogram(conn_matrix, conn_model, atlas_select, dir_path, ID,
network, label_names):
import json
from networkx.readwrite import json_graph
from pathlib import Path
from pynets.thresholding import normalize
from pynets.netstats import most_important
from scipy.cluster.hierarchy import linkage, fcluster
from nipype.utils.filemanip import save_json
##Advanced Settings
comm = 'nodes'
pruned = False
#color_scheme = 'interpolateCool'
#color_scheme = 'interpolateGnBu'
#color_scheme = 'interpolateOrRd'
#color_scheme = 'interpolatePuRd'
#color_scheme = 'interpolateYlOrRd'
#color_scheme = 'interpolateReds'
#color_scheme = 'interpolateGreens'
color_scheme = 'interpolateBlues'
##Advanced Settings
conn_matrix = normalize(conn_matrix)
G = nx.from_numpy_matrix(conn_matrix)
if pruned == True:
[G, pruned_nodes, pruned_edges] = most_important(G)
conn_matrix = nx.to_numpy_array(G)
pruned_nodes.sort(reverse=True)
for j in pruned_nodes:
del label_names[label_names.index(label_names[j])]
pruned_edges.sort(reverse=True)
for j in pruned_edges:
del label_names[label_names.index(label_names[j])]
def doClust(X, clust_levels):
##get the linkage diagram
Z = linkage(
X,
'ward',
)
##choose # cluster levels
cluster_levels = range(1, int(clust_levels))
##init array to store labels for each level
clust_levels_tmp = int(clust_levels) - 1
label_arr = np.zeros((int(clust_levels_tmp), int(X.shape[0])))
##iterate thru levels
for c in cluster_levels:
fl = fcluster(Z, c, criterion='maxclust')
#print(fl)
label_arr[c - 1, :] = fl
return label_arr, clust_levels_tmp
if comm == 'nodes' and len(conn_matrix) > 40:
from pynets.netstats import modularity_louvain_dir
if len(conn_matrix) < 50:
gamma = 0.00001
elif len(conn_matrix) < 100:
gamma = 0.0001
elif len(conn_matrix) < 200:
gamma = 0.001
elif len(conn_matrix) < 500:
gamma = 0.01
elif len(conn_matrix) < 1000:
gamma = 0.5
else:
gamma = 1
[node_comm_aff_mat, q] = modularity_louvain_dir(conn_matrix,
hierarchy=True,
gamma=gamma)
print('Found ' + str(len(np.unique(node_comm_aff_mat))) +
' communities with gamma=' + str(gamma) + '...')
clust_levels = len(node_comm_aff_mat)
clust_levels_tmp = int(clust_levels) - 1
mask_mat = np.squeeze(np.array([node_comm_aff_mat == 0]).astype('int'))
label_arr = node_comm_aff_mat * np.expand_dims(
np.arange(1, clust_levels + 1), axis=1) + mask_mat
elif comm == 'links' and len(conn_matrix) > 40:
from pynets.netstats import link_communities
##Plot link communities
link_comm_aff_mat = link_communities(conn_matrix,
type_clustering='single')
print('Found ' + str(len(link_comm_aff_mat)) + ' communities...')
clust_levels = len(link_comm_aff_mat)
clust_levels_tmp = int(clust_levels) - 1
mask_mat = np.squeeze(np.array([link_comm_aff_mat == 0]).astype('int'))
label_arr = link_comm_aff_mat * np.expand_dims(
np.arange(1, clust_levels + 1), axis=1) + mask_mat
elif len(conn_matrix) > 20:
print(
'Graph too small for reliable plotting of communities. Plotting by fcluster instead...'
)
if len(conn_matrix) >= 250:
clust_levels = 7
elif len(conn_matrix) >= 200:
clust_levels = 6
elif len(conn_matrix) >= 150:
clust_levels = 5
elif len(conn_matrix) >= 100:
clust_levels = 4
elif len(conn_matrix) >= 50:
clust_levels = 3
else:
clust_levels = 2
[label_arr, clust_levels_tmp] = doClust(conn_matrix, clust_levels)
def get_node_label(node_idx, labels, clust_levels_tmp):
from collections import OrderedDict
def write_roman(num):
roman = OrderedDict()
roman[1000] = "M"
roman[900] = "CM"
roman[500] = "D"
roman[400] = "CD"
roman[100] = "C"
roman[90] = "XC"
roman[50] = "L"
roman[40] = "XL"
roman[10] = "X"
roman[9] = "IX"
roman[5] = "V"
roman[4] = "IV"
roman[1] = "I"
def roman_num(num):
for r in roman.keys():
x, y = divmod(num, r)
yield roman[r] * x
num -= (r * x)
if num > 0:
roman_num(num)
else:
break
return "".join([a for a in roman_num(num)])
rn_list = []
node_idx = node_idx - 1
node_labels = labels[:, node_idx]
for i in [int(l) for i, l in enumerate(node_labels)]:
rn_list.append(json.dumps(write_roman(i)))
abet = rn_list
return ".".join([
"{}{}".format(abet[i], int(l)) for i, l in enumerate(node_labels)
]) + ".{}".format(label_names[node_idx])
output = []
adj_dict = {}
for i in list(G.adjacency()):
source = list(i)[0]
target = list(list(i)[1])
adj_dict[source] = target
for node_idx, connections in adj_dict.items():
weight_vec = []
for i in connections:
wei = G.get_edge_data(node_idx, int(i))['weight']
weight_vec.append(wei)
entry = {}
nodes_label = get_node_label(node_idx, label_arr, clust_levels_tmp)
entry["name"] = nodes_label
entry["size"] = len(connections)
entry["imports"] = [
get_node_label(int(d) - 1, label_arr, clust_levels_tmp)
for d in connections
]
entry["weights"] = weight_vec
output.append(entry)
if network:
json_file_name = str(
ID
) + '_' + network + '_connectogram_' + conn_model + '_network.json'
json_fdg_file_name = str(
ID) + '_' + network + '_fdg_' + conn_model + '_network.json'
connectogram_plot = dir_path + '/' + json_file_name
fdg_js_sub = dir_path + '/' + str(
ID) + '_' + network + '_fdg_' + conn_model + '_network.js'
fdg_js_sub_name = str(
ID) + '_' + network + '_fdg_' + conn_model + '_network.js'
connectogram_js_sub = dir_path + '/' + str(
ID) + '_' + network + '_connectogram_' + conn_model + '_network.js'
connectogram_js_name = str(
ID) + '_' + network + '_connectogram_' + conn_model + '_network.js'
else:
json_file_name = str(ID) + '_connectogram_' + conn_model + '.json'
json_fdg_file_name = str(ID) + '_fdg_' + conn_model + '.json'
connectogram_plot = dir_path + '/' + json_file_name
connectogram_js_sub = dir_path + '/' + str(
ID) + '_connectogram_' + conn_model + '.js'
fdg_js_sub = dir_path + '/' + str(ID) + '_fdg_' + conn_model + '.js'
fdg_js_sub_name = str(ID) + '_fdg_' + conn_model + '.js'
connectogram_js_name = str(ID) + '_connectogram_' + conn_model + '.js'
save_json(connectogram_plot, output)
##Force-directed graphing
G = nx.from_numpy_matrix(np.round(conn_matrix.astype('float64'), 6))
data = json_graph.node_link_data(G)
data.pop('directed', None)
data.pop('graph', None)
data.pop('multigraph', None)
for k in range(len(data['links'])):
data['links'][k]['value'] = data['links'][k].pop('weight')
for k in range(len(data['nodes'])):
data['nodes'][k]['id'] = str(data['nodes'][k]['id'])
for k in range(len(data['links'])):
data['links'][k]['source'] = str(data['links'][k]['source'])
data['links'][k]['target'] = str(data['links'][k]['target'])
##Add community structure
for k in range(len(data['nodes'])):
data['nodes'][k]['group'] = str(label_arr[0][k])
##Add node labels
for k in range(len(data['nodes'])):
data['nodes'][k]['name'] = str(label_names[k])
out_file = str(dir_path + '/' + json_fdg_file_name)
save_json(out_file, data)
##Copy index.html and json to dir_path
#conn_js_path = '/Users/PSYC-dap3463/Applications/PyNets/pynets/connectogram.js'
#index_html_path = '/Users/PSYC-dap3463/Applications/PyNets/pynets/index.html'
conn_js_path = str(Path(__file__).parent / "connectogram.js")
index_html_path = str(Path(__file__).parent / "index.html")
fdg_replacements_js = {"FD_graph.json": str(json_fdg_file_name)}
replacements_html = {
'connectogram.js': str(connectogram_js_name),
'fdg.js': str(fdg_js_sub_name)
}
fdg_js_path = str(Path(__file__).parent / "fdg.js")
with open(index_html_path) as infile, open(str(dir_path + '/index.html'),
'w') as outfile:
for line in infile:
for src, target in replacements_html.items():
line = line.replace(src, target)
outfile.write(line)
replacements_js = {
'template.json': str(json_file_name),
'interpolateCool': str(color_scheme)
}
with open(conn_js_path) as infile, open(connectogram_js_sub,
'w') as outfile:
for line in infile:
for src, target in replacements_js.items():
line = line.replace(src, target)
outfile.write(line)
with open(fdg_js_path) as infile, open(fdg_js_sub, 'w') as outfile:
for line in infile:
for src, target in fdg_replacements_js.items():
line = line.replace(src, target)
outfile.write(line)
def test_identity_weighted_digraph_array(self):
"""Conversion from weighted digraph to array to weighted digraph."""
A = nx.to_numpy_array(self.G4)
self.identity_conversion(self.G4, A, nx.DiGraph())
def test_identity_weighted_digraph_array(self):
"""Conversion from weighted digraph to array to weighted digraph."""
A = nx.to_numpy_array(self.G4)
self.identity_conversion(self.G4, A, nx.DiGraph())
def plot_all(conn_matrix, conn_model, atlas_select, dir_path, ID, network,
label_names, mask, coords, thr, node_size, edge_threshold):
import matplotlib
matplotlib.use('Agg')
from matplotlib import pyplot as plt
from nilearn import plotting as niplot
pruning = True
dpi_resolution = 1000
import pkg_resources
import networkx as nx
from pynets import plotting
from pynets.netstats import most_important
G_pre = nx.from_numpy_matrix(conn_matrix)
if pruning == True:
[G, pruned_nodes, pruned_edges] = most_important(G_pre)
else:
G = G_pre
conn_matrix = nx.to_numpy_array(G)
pruned_nodes.sort(reverse=True)
for j in pruned_nodes:
del label_names[label_names.index(label_names[j])]
del coords[coords.index(coords[j])]
pruned_edges.sort(reverse=True)
for j in pruned_edges:
del label_names[label_names.index(label_names[j])]
del coords[coords.index(coords[j])]
##Plot connectogram
if len(conn_matrix) > 20:
try:
plotting.plot_connectogram(conn_matrix, conn_model, atlas_select,
dir_path, ID, network, label_names)
except RuntimeError:
print('\n\n\nError: Connectogram plotting failed!')
else:
print(
'Error: Cannot plot connectogram for graphs smaller than 20 x 20!')
##Plot adj. matrix based on determined inputs
plotting.plot_conn_mat(conn_matrix, conn_model, atlas_select, dir_path, ID,
network, label_names, mask, thr, node_size)
##Plot connectome
if mask:
if network:
out_path_fig = dir_path + '/' + ID + '_' + str(
atlas_select) + '_' + str(conn_model) + '_' + str(
os.path.basename(mask).split('.')[0]) + '_' + str(
network) + '_' + str(thr) + '_' + str(
node_size) + '_connectome_viz.png'
else:
out_path_fig = dir_path + '/' + ID + '_' + str(
atlas_select) + '_' + str(conn_model) + '_' + str(
os.path.basename(mask).split('.')[0]) + '_' + str(
thr) + '_' + str(node_size) + '_connectome_viz.png'
else:
if network:
out_path_fig = dir_path + '/' + ID + '_' + str(
atlas_select) + '_' + str(conn_model) + '_' + str(
network) + '_' + str(thr) + '_' + str(
node_size) + '_connectome_viz.png'
else:
out_path_fig = dir_path + '/' + ID + '_' + str(
atlas_select) + '_' + str(conn_model) + '_' + str(
thr) + '_' + str(node_size) + '_connectome_viz.png'
#niplot.plot_connectome(conn_matrix, coords, edge_threshold=edge_threshold, node_size=20, colorbar=True, output_file=out_path_fig)
ch2better_loc = pkg_resources.resource_filename(
"pynets", "templates/ch2better.nii.gz")
connectome = niplot.plot_connectome(np.zeros(shape=(1, 1)), [(0, 0, 0)],
black_bg=True,
node_size=0.0001)
connectome.add_overlay(ch2better_loc, alpha=0.4, cmap=plt.cm.gray)
[z_min, z_max] = -np.abs(conn_matrix).max(), np.abs(conn_matrix).max()
connectome.add_graph(conn_matrix,
coords,
edge_threshold=edge_threshold,
edge_cmap='Greens',
edge_vmax=z_max,
edge_vmin=z_min,
node_size=4)
connectome.savefig(out_path_fig, dpi=dpi_resolution)
return
def subgraph_centrality(G):
r"""Returns subgraph centrality for each node in G.
Subgraph centrality of a node `n` is the sum of weighted closed
walks of all lengths starting and ending at node `n`. The weights
decrease with path length. Each closed walk is associated with a
connected subgraph ([1]_).
Parameters
----------
G: graph
Returns
-------
nodes : dictionary
Dictionary of nodes with subgraph centrality as the value.
Raises
------
NetworkXError
If the graph is not undirected and simple.
See Also
--------
subgraph_centrality_exp:
Alternative algorithm of the subgraph centrality for each node of G.
Notes
-----
This version of the algorithm computes eigenvalues and eigenvectors
of the adjacency matrix.
Subgraph centrality of a node `u` in G can be found using
a spectral decomposition of the adjacency matrix [1]_,
.. math::
SC(u)=\sum_{j=1}^{N}(v_{j}^{u})^2 e^{\lambda_{j}},
where `v_j` is an eigenvector of the adjacency matrix `A` of G
corresponding to the eigenvalue `\lambda_j`.
Examples
--------
(Example from [1]_)
>>> G = nx.Graph(
... [
... (1, 2),
... (1, 5),
... (1, 8),
... (2, 3),
... (2, 8),
... (3, 4),
... (3, 6),
... (4, 5),
... (4, 7),
... (5, 6),
... (6, 7),
... (7, 8),
... ]
... )
>>> sc = nx.subgraph_centrality(G)
>>> print([f"{node} {sc[node]:0.2f}" for node in sorted(sc)])
['1 3.90', '2 3.90', '3 3.64', '4 3.71', '5 3.64', '6 3.71', '7 3.64', '8 3.90']
References
----------
.. [1] Ernesto Estrada, Juan A. Rodriguez-Velazquez,
"Subgraph centrality in complex networks",
Physical Review E 71, 056103 (2005).
https://arxiv.org/abs/cond-mat/0504730
"""
import numpy as np
nodelist = list(G) # ordering of nodes in matrix
A = nx.to_numpy_array(G, nodelist)
# convert to 0-1 matrix
A[np.nonzero(A)] = 1
w, v = np.linalg.eigh(A)
vsquare = np.array(v)**2
expw = np.exp(w)
xg = vsquare @ expw
# convert vector dictionary keyed by node
sc = dict(zip(nodelist, map(float, xg)))
return sc
print(
f"Preprocessed graph {graph_type} with threshold={threshold}, weight={weight}"
)
out_classes = [
"O_dVNC",
"O_dSEZ",
"O_IPC",
"O_ITP",
"O_dSEZ;FFN",
"O_CA-LP",
"O_dSEZ;FB2N",
]
sens_classes = ["sens"]
adj = nx.to_numpy_array(mg.g, weight=weight, nodelist=mg.meta.index.values)
prob_mat = adj.copy()
row_sums = prob_mat.sum(axis=1)
dead_inds = np.where(row_sums == 0)[0]
row_sums[row_sums == 0] = 1
prob_mat = prob_mat / row_sums[:, np.newaxis]
n_verts = len(prob_mat)
meta = mg.meta.copy()
g = mg.g.copy()
meta["idx"] = range(len(meta))
from_inds = meta[meta["Class 1"].isin(sens_classes)]["idx"].values
out_inds = meta[meta["Class 1"].isin(out_classes)]["idx"].values
ind_map = dict(zip(meta.index, meta["idx"]))
g = nx.relabel_nodes(g, ind_map, copy=True)
def subgraph_centrality_exp(G):
r"""Returns the subgraph centrality for each node of G.
Subgraph centrality of a node `n` is the sum of weighted closed
walks of all lengths starting and ending at node `n`. The weights
decrease with path length. Each closed walk is associated with a
connected subgraph ([1]_).
Parameters
----------
G: graph
Returns
-------
nodes:dictionary
Dictionary of nodes with subgraph centrality as the value.
Raises
------
NetworkXError
If the graph is not undirected and simple.
See Also
--------
subgraph_centrality:
Alternative algorithm of the subgraph centrality for each node of G.
Notes
-----
This version of the algorithm exponentiates the adjacency matrix.
The subgraph centrality of a node `u` in G can be found using
the matrix exponential of the adjacency matrix of G [1]_,
.. math::
SC(u)=(e^A)_{uu} .
References
----------
.. [1] Ernesto Estrada, Juan A. Rodriguez-Velazquez,
"Subgraph centrality in complex networks",
Physical Review E 71, 056103 (2005).
https://arxiv.org/abs/cond-mat/0504730
Examples
--------
(Example from [1]_)
>>> G = nx.Graph(
... [
... (1, 2),
... (1, 5),
... (1, 8),
... (2, 3),
... (2, 8),
... (3, 4),
... (3, 6),
... (4, 5),
... (4, 7),
... (5, 6),
... (6, 7),
... (7, 8),
... ]
... )
>>> sc = nx.subgraph_centrality_exp(G)
>>> print([f"{node} {sc[node]:0.2f}" for node in sorted(sc)])
['1 3.90', '2 3.90', '3 3.64', '4 3.71', '5 3.64', '6 3.71', '7 3.64', '8 3.90']
"""
# alternative implementation that calculates the matrix exponential
import scipy as sp
import scipy.linalg # call as sp.linalg
nodelist = list(G) # ordering of nodes in matrix
A = nx.to_numpy_array(G, nodelist)
# convert to 0-1 matrix
A[A != 0.0] = 1
expA = sp.linalg.expm(A)
# convert diagonal to dictionary keyed by node
sc = dict(zip(nodelist, map(float, expA.diagonal())))
return sc
def notears_live(G: nx.DiGraph,
X: np.ndarray,
lambda1: float,
max_iter: int = 100,
h_tol: float = 1e-8,
w_threshold: float = 0.3) -> np.ndarray:
"""Monitor the optimization progress live in notebook.
Args:
G: ground truth graph
X: [n,d] sample matrix
lambda1: l1 regularization parameter
max_iter: max number of dual ascent steps
h_tol: exit if |h(w)| <= h_tol
w_threshold: fixed threshold for edge weights
Returns:
W_est: [d,d] estimate
"""
# initialization
n, d = X.shape
w_est, w_new = np.zeros(d * d), np.zeros(d * d)
rho, alpha, h, h_new = 1.0, 0.0, np.inf, np.inf
# ground truth
w_true = nx.to_numpy_array(G).flatten()
# progress, stream
progress_data = {
key: []
for key in ['step', 'F', 'h', 'rho', 'alpha', 'l2_dist']
}
progress_source = ColumnDataSource(data=progress_data)
# heatmap, patch
ids = [str(i) for i in range(d)]
all_ids = np.tile(ids, [d, 1])
row = all_ids.T.flatten()
col = all_ids.flatten()
heatmap_data = {
'row': row,
'col': col,
'w_true': w_true,
'w_est': w_est,
'w_diff': w_true - w_est
}
heatmap_source = ColumnDataSource(data=heatmap_data)
mapper = LinearColorMapper(palette=Palette, low=-2, high=2)
# common tools
tools = 'crosshair,save,reset'
# F(w_est) vs step
F_true = cppext.F_func(w_true, X, lambda1)
fig0 = figure(plot_width=270,
plot_height=240,
y_axis_type='log',
tools=tools)
fig0.ray(0,
F_true,
length=0,
angle=0,
color='green',
line_dash='dashed',
line_width=2,
legend='F(w_true)')
fig0.line('step',
'F',
source=progress_source,
color='red',
line_width=2,
legend='F(w_est)')
fig0.title.text = "Objective"
fig0.xaxis.axis_label = "step"
fig0.legend.location = "bottom_left"
fig0.legend.background_fill_alpha = 0.5
fig0.add_tools(
HoverTool(tooltips=[("step", "@step"), ("F", "@F"),
("F_true", '%.6g' % F_true)],
mode='vline'))
# h(w_est) vs step
fig1 = figure(plot_width=280,
plot_height=240,
y_axis_type='log',
tools=tools)
fig1.line('step',
'h',
source=progress_source,
color='magenta',
line_width=2,
legend='h(w_est)')
fig1.title.text = "Constraint"
fig1.xaxis.axis_label = "step"
fig1.legend.location = "bottom_left"
fig1.legend.background_fill_alpha = 0.5
fig1.add_tools(
HoverTool(tooltips=[("step", "@step"), ("h", "@h"), ("rho", "@rho"),
("alpha", "@alpha")],
mode='vline'))
# ||w_true - w_est|| vs step
fig2 = figure(plot_width=270,
plot_height=240,
y_axis_type='log',
tools=tools)
fig2.line('step',
'l2_dist',
source=progress_source,
color='blue',
line_width=2)
fig2.title.text = "L2 distance to W_true"
fig2.xaxis.axis_label = "step"
fig2.add_tools(
HoverTool(tooltips=[("step", "@step"), ("w_est", "@l2_dist")],
mode='vline'))
# heatmap of w_true
fig3 = figure(plot_width=270,
plot_height=240,
x_range=ids,
y_range=list(reversed(ids)),
tools=tools)
fig3.rect(x='col',
y='row',
width=1,
height=1,
source=heatmap_source,
line_color=None,
fill_color=transform('w_true', mapper))
fig3.title.text = 'W_true'
fig3.axis.visible = False
fig3.add_tools(
HoverTool(tooltips=[("row, col", "@row, @col"), ("w_true",
"@w_true")]))
# heatmap of w_est
fig4 = figure(plot_width=280,
plot_height=240,
x_range=ids,
y_range=list(reversed(ids)),
tools=tools)
fig4.rect(x='col',
y='row',
width=1,
height=1,
source=heatmap_source,
line_color=None,
fill_color=transform('w_est', mapper))
fig4.title.text = 'W_est'
fig4.axis.visible = False
fig4.add_tools(
HoverTool(tooltips=[("row, col", "@row, @col"), ("w_est", "@w_est")]))
# heatmap of w_true - w_est
fig5 = figure(plot_width=270,
plot_height=240,
x_range=ids,
y_range=list(reversed(ids)),
tools=tools)
fig5.rect(x='col',
y='row',
width=1,
height=1,
source=heatmap_source,
line_color=None,
fill_color=transform('w_diff', mapper))
fig5.title.text = 'W_true - W_est'
fig5.axis.visible = False
fig5.add_tools(
HoverTool(tooltips=[("row, col", "@row, @col"), ("w_diff",
"@w_diff")]))
# display figures as grid
grid = gridplot([[fig0, fig1, fig2], [fig3, fig4, fig5]],
merge_tools=False)
handle = show(grid, notebook_handle=True)
# enter main loop
for it in range(max_iter):
while rho < 1e+20:
w_new = cppext.minimize_subproblem(w_est, X, rho, alpha, lambda1)
h_new = cppext.h_func(w_new)
if h_new > 0.25 * h:
rho *= 10
else:
break
w_est, h = w_new, h_new
alpha += rho * h
# update figures
progress_source.stream({
'step': [it],
'F': [cppext.F_func(w_est, X, lambda1)],
'h': [h],
'rho': [rho],
'alpha': [alpha],
'l2_dist': [np.linalg.norm(w_est - w_true)],
})
heatmap_source.patch({
'w_est': [(slice(d * d), w_est)],
'w_diff': [(slice(d * d), w_true - w_est)]
})
push_notebook(handle=handle)
# check termination of main loop
if h <= h_tol:
break
# final threshold
w_est[np.abs(w_est) < w_threshold] = 0
return w_est.reshape([d, d])
def communicability_betweenness_centrality(G):
r"""Returns subgraph communicability for all pairs of nodes in G.
Communicability betweenness measure makes use of the number of walks
connecting every pair of nodes as the basis of a betweenness centrality
measure.
Parameters
----------
G: graph
Returns
-------
nodes : dictionary
Dictionary of nodes with communicability betweenness as the value.
Raises
------
NetworkXError
If the graph is not undirected and simple.
Notes
-----
Let `G=(V,E)` be a simple undirected graph with `n` nodes and `m` edges,
and `A` denote the adjacency matrix of `G`.
Let `G(r)=(V,E(r))` be the graph resulting from
removing all edges connected to node `r` but not the node itself.
The adjacency matrix for `G(r)` is `A+E(r)`, where `E(r)` has nonzeros
only in row and column `r`.
The subraph betweenness of a node `r` is [1]_
.. math::
\omega_{r} = \frac{1}{C}\sum_{p}\sum_{q}\frac{G_{prq}}{G_{pq}},
p\neq q, q\neq r,
where
`G_{prq}=(e^{A}_{pq} - (e^{A+E(r)})_{pq}` is the number of walks
involving node r,
`G_{pq}=(e^{A})_{pq}` is the number of closed walks starting
at node `p` and ending at node `q`,
and `C=(n-1)^{2}-(n-1)` is a normalization factor equal to the
number of terms in the sum.
The resulting `\omega_{r}` takes values between zero and one.
The lower bound cannot be attained for a connected
graph, and the upper bound is attained in the star graph.
References
----------
.. [1] Ernesto Estrada, Desmond J. Higham, Naomichi Hatano,
"Communicability Betweenness in Complex Networks"
Physica A 388 (2009) 764-774.
https://arxiv.org/abs/0905.4102
Examples
--------
>>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)])
>>> cbc = nx.communicability_betweenness_centrality(G)
>>> print([f"{node} {cbc[node]:0.2f}" for node in sorted(cbc)])
['0 0.03', '1 0.45', '2 0.51', '3 0.45', '4 0.40', '5 0.19', '6 0.03']
"""
import numpy as np
import scipy as sp
import scipy.linalg # call as sp.linalg
nodelist = list(G) # ordering of nodes in matrix
n = len(nodelist)
A = nx.to_numpy_array(G, nodelist)
# convert to 0-1 matrix
A[np.nonzero(A)] = 1
expA = sp.linalg.expm(A)
mapping = dict(zip(nodelist, range(n)))
cbc = {}
for v in G:
# remove row and col of node v
i = mapping[v]
row = A[i, :].copy()
col = A[:, i].copy()
A[i, :] = 0
A[:, i] = 0
B = (expA - sp.linalg.expm(A)) / expA
# sum with row/col of node v and diag set to zero
B[i, :] = 0
B[:, i] = 0
B -= np.diag(np.diag(B))
cbc[v] = float(B.sum())
# put row and col back
A[i, :] = row
A[:, i] = col
# rescale when more than two nodes
order = len(cbc)
if order > 2:
scale = 1.0 / ((order - 1.0)**2 - (order - 1.0))
for v in cbc:
cbc[v] *= scale
return cbc
def load(dataset):
basedir = os.path.dirname(os.path.abspath(__file__))
datadir = os.path.join(basedir, 'data', dataset)
print(datadir)
if not os.path.exists(datadir):
download(dataset)
graphs, diff = process(dataset)
feat, adj, labels = [], [], []
for idx, graph in enumerate(graphs):
adj.append(nx.to_numpy_array(graph))
labels.append(graph.graph['label'])
feat.append(
np.array(list(nx.get_node_attributes(graph, 'feat').values())))
adj, diff, feat, labels = np.array(adj), np.array(diff), np.array(
feat), np.array(labels)
np.save(f'{datadir}/adj.npy', adj)
#np.save(f'{datadir}/diff.npy', diff)
np.save(f'{datadir}/feat.npy', feat)
np.save(f'{datadir}/labels.npy', labels)
else:
adj = np.load(f'{datadir}/adj.npy', allow_pickle=True)
#diff = np.load(f'{datadir}/diff.npy', allow_pickle=True)
feat = np.load(f'{datadir}/feat.npy', allow_pickle=True)
labels = np.load(f'{datadir}/labels.npy', allow_pickle=True)
max_nodes = max([a.shape[0] for a in adj])
feat_dim = feat[0].shape[-1]
num_nodes = []
#import pdb;pdb.set_trace()
for idx in range(adj.shape[0]):
num_nodes.append(adj[idx].shape[-1])
#adj[idx] = normalize_adj(adj[idx]).todense()
#diff[idx] = sparse.csr_matrix(np.hstack(
# (np.vstack((diff[idx], np.zeros((max_nodes - diff[idx].shape[0], diff[idx].shape[0])))),
# np.zeros((max_nodes, max_nodes - diff[idx].shape[1])))))
diff = []
adj[idx] = sparse.csr_matrix(
np.hstack((np.vstack(
(adj[idx],
np.zeros(
(max_nodes - adj[idx].shape[0], adj[idx].shape[0])))),
np.zeros((max_nodes, max_nodes - adj[idx].shape[1])))))
feat[idx] = sparse.csr_matrix(
np.vstack(
(feat[idx], np.zeros(
(max_nodes - feat[idx].shape[0], feat_dim)))))
#adj = np.array(adj.tolist()).reshape(-1, max_nodes, max_nodes)
#diff = np.array(diff.tolist()).reshape(-1, max_nodes, max_nodes)
#feat = np.array(feat.tolist()).reshape(-1, max_nodes, feat_dim)
#import pdb; pdb.set_trace()
return adj, diff, feat, labels, num_nodes
def load_pubmed(feature_dim, initializer):
#hardcoded for simplicity...
num_nodes = 19717
num_feats = feature_dim if initializer != 'None' else 500
num_classes = 3
train_size = num_classes * 20
if initializer == "1hot":
num_feats = num_nodes
feat_data = np.zeros((num_nodes, num_feats))
labels = np.empty((num_nodes, 1), dtype=np.int64)
node_map = {}
label_map = {}
label_node_list_map = {}
train_idx = []
test_idx = []
val_idx = []
if initializer == "None":
with open("pubmed-data/Pubmed-Diabetes.NODE.paper.tab") as fp:
fp.readline()
feat_map = {
entry.split(":")[1]: i - 1
for i, entry in enumerate(fp.readline().split("\t"))
}
for i, line in enumerate(fp):
info = line.split("\t")
node_map[info[0]] = i
labels[i] = int(info[1].split("=")[1]) - 1
if labels[i][0] not in label_node_list_map:
label_node_list_map[labels[i][0]] = []
label_node_list_map[labels[i][0]].append(i)
for word_info in info[2:-1]:
word_info = word_info.split("=")
feat_data[i][feat_map[word_info[0]]] = float(word_info[1])
else:
with open("pubmed-data/Pubmed-Diabetes.NODE.paper.tab") as fp:
fp.readline()
fp.readline()
for i, line in enumerate(fp):
info = line.split("\t")
node_map[info[0]] = i
labels[i] = int(info[1].split("=")[1]) - 1
if labels[i][0] not in label_node_list_map:
label_node_list_map[labels[i][0]] = []
label_node_list_map[labels[i][0]].append(i)
# set initializer method
if initializer == "1hot":
feat_data = np.eye(num_nodes)
elif initializer == "random_normal":
feat_data = np.random.normal(0, 1, (num_nodes, feature_dim))
elif initializer == "shared":
feat_data = np.ones((num_nodes, feature_dim))
elif initializer == "node_degree":
feat_data = np.zeros((num_nodes, 1))
elif initializer == "3371" or "eigen" in initializer or initializer == "pagerank":
G = nx.Graph()
G.add_nodes_from(node_map.values())
elif initializer == "deepwalk":
feat_data = extract_deepwalk_embeddings(
"pubmed-data/pubmed_{dim}.embeddings".format(dim=feature_dim),
node_map)
adj_lists = defaultdict(set)
with open("pubmed-data/Pubmed-Diabetes.DIRECTED.cites.tab") as fp:
fp.readline()
fp.readline()
for line in fp:
info = line.strip().split("\t")
paper1 = node_map[info[1].split(":")[1]]
paper2 = node_map[info[-1].split(":")[1]]
adj_lists[paper1].add(paper2)
adj_lists[paper2].add(paper1)
if initializer == "pagerank" or initializer == "eigen":
G.add_edge(paper1, paper2)
G.add_edge(paper2, paper1)
if initializer == "node_degree":
# convert to 1hot representation
node_degrees = [len(v) for v in adj_lists.values()]
max_degree = max(node_degrees)
feat_data = np.zeros((num_nodes, max_degree + 1))
for k, v in adj_lists.items():
feat_data[k, len(v)] = 1
elif initializer == "pagerank":
feat_data = np.zeros((num_nodes, feature_dim))
pagerank = nx.pagerank(G)
for k, v in pagerank.items():
feat_data[k, :] = v
elif "eigen" in initializer:
try:
if initializer == "eigen":
v = np.load("pubmed-data/pubmed_eigenvector.npy")
else:
v = np.load(
"pubmed-data/pubmed_eigenvector_degree_normalized.npy")
print(v.shape)
except:
adj_matrix = nx.to_numpy_array(G)
# normalize adjacency matrix with degree
if initializer == "eigen_norm":
sum_of_rows = adj_matrix.sum(axis=1)
adj_matrix = adj_matrix / sum_of_rows[:, None]
print("start computing eigen vectors")
w, v = LA.eig(adj_matrix)
indices = np.argsort(w)[::-1]
v = v.transpose()[indices]
# only save top 1000 eigenvectors
if initializer == "eigen":
np.save("pubmed-data/pubmed_eigenvector", v[:1000])
else:
np.save("pubmed-data/pubmed_eigenvector_degree_normalized",
v[:1000])
# print(v)
feat_data = np.zeros((num_nodes, feature_dim))
# assert(feature_dim <= 1000)
for i in range(num_nodes):
for j in range(feature_dim):
feat_data[i, j] = v[j, i]
for label, node_list in label_node_list_map.items():
random.shuffle(node_list)
train_idx.extend(node_list[:20])
anchor = 20 + int(500 / num_classes)
val_idx.extend(node_list[20:anchor])
test_idx.extend(node_list[anchor:])
return feat_data, labels, train_idx, test_idx, val_idx, adj_lists
def test_graphin(self):
G = nx.from_numpy_array(self.A)
np.testing.assert_array_equal(nx.to_numpy_array(G), gus.import_graph(G))
def load_citeseer(feature_dim, initializer="None"):
'''
hard coded for simplicity
'''
num_nodes = 3312
num_feats = feature_dim if initializer != 'None' else 3703
num_classes = 6
train_size = num_classes * 20
if initializer == "1hot":
num_feats = num_nodes
feat_data = np.zeros((num_nodes, num_feats))
labels = np.empty((num_nodes, 1), dtype=np.int64)
node_map = {}
label_map = {}
label_node_list_map = {}
train_idx = []
test_idx = []
val_idx = []
if initializer == "None":
with open("citeseer/citeseer.content") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
# print(len(list(map(float, info[1:-1]))))
feat_data[i, :] = list(map(float, info[1:-1]))
print(feat_data[i, :].shape)
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
else:
print("Initializing with", initializer)
with open("citeseer/citeseer.content") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
# set initializer method
if initializer == "1hot":
feat_data = np.eye(num_nodes)
elif initializer == "random_normal":
feat_data = np.random.normal(0, 1, (num_nodes, feature_dim))
elif initializer == "shared":
feat_data = np.ones((num_nodes, feature_dim))
elif initializer == "node_degree":
feat_data = np.zeros((num_nodes, 1))
elif initializer == "pagerank" or "eigen" in initializer:
G = nx.Graph()
G.add_nodes_from(node_map.values())
elif initializer == "deepwalk":
feat_data = extract_deepwalk_embeddings(
"citeseer/citeseer_{dim}.embeddings".format(dim=feature_dim),
node_map, "citeseer")
adj_lists = defaultdict(set)
with open("citeseer/citeseer.cites") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
try:
paper1 = node_map[info[0]]
paper2 = node_map[info[1]]
except:
# print(info[0], info[1])
continue
adj_lists[paper1].add(paper2)
adj_lists[paper2].add(paper1)
if initializer == "pagerank" or initializer == "eigen":
G.add_edge(paper1, paper2)
G.add_edge(paper2, paper1)
if initializer == "node_degree":
# convert to 1hot representation
node_degrees = [len(v) for v in adj_lists.values()]
max_degree = max(node_degrees)
feat_data = np.zeros((num_nodes, max_degree + 1))
for k, v in adj_lists.items():
feat_data[k, len(v)] = 1
elif initializer == "pagerank":
feat_data = np.zeros((num_nodes, feature_dim))
pagerank = nx.pagerank(G)
for k, v in pagerank.items():
feat_data[k, :] = v
elif "eigen" in initializer:
try:
if initializer == "eigen":
v = np.load("citeseer/citeseer_eigenvector.npy")
else:
v = np.load(
"citeseer/citeseer_eigenvector_degree_normalized.npy")
print(v.shape)
except:
adj_matrix = nx.to_numpy_array(G)
# normalize adjacency matrix with degree
if initializer == "eigen_norm":
sum_of_rows = adj_matrix.sum(axis=1)
adj_matrix = adj_matrix / sum_of_rows[:, None]
print("start computing eigen vectors")
w, v = LA.eig(adj_matrix)
indices = np.argsort(w)[::-1]
v = v.transpose()[indices]
# only save top 1000 eigenvectors
if initializer == "eigen":
np.save("citeseer/citeseer_eigenvector", v[:1000])
else:
np.save("citeseer/citeseer_eigenvector_degree_normalized",
v[:1000])
# for j in range(0, 5):
# count = 0
# for i in range(v.shape[1]):
# if v[j, i].real < 1e-200 and v[j, i].real > 0:
# print("real part smaller than 1e-200", j, i, v[j, i])
# count += 1
# print(j, count)
adj_matrix = nx.to_numpy_array(G)
v = v.real
# zeros = 3312-np.count_nonzero(v, axis=1)
# np.savetxt("citeseer_eigenvector_nonzeros.txt", zeros, fmt="%d")
# plt.bar(range(len(zeros)), zeros)
# plt.xlabel("node index")
# plt.ylabel("number of zeros in eigenvectors")
# plt.savefig('plot.png', dpi=300, bbox_inches='tight')
# plt.show()
feat_data = np.zeros((num_nodes, feature_dim))
# assert(feature_dim <= 1000)
for i in range(num_nodes):
for j in range(feature_dim):
feat_data[i, j] = v[j, i]
for label, node_list in label_node_list_map.items():
random.shuffle(node_list)
train_idx.extend(node_list[:20])
anchor = 20 + int(500 / num_classes)
val_idx.extend(node_list[20:anchor])
test_idx.extend(node_list[anchor:])
return feat_data, labels, train_idx, test_idx, val_idx, adj_lists
def fruchterman_reingold_layout(G,
k=None,
pos=None,
fixed=None,
iterations=50,
threshold=1e-4,
weight='weight',
scale=1,
center=None,
dim=2,
seed=None):
"""Position nodes using Fruchterman-Reingold force-directed algorithm.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
k : float (default=None)
Optimal distance between nodes. If None the distance is set to
1/sqrt(n) where n is the number of nodes. Increase this value
to move nodes farther apart.
pos : dict or None optional (default=None)
Initial positions for nodes as a dictionary with node as keys
and values as a coordinate list or tuple. If None, then use
random initial positions.
fixed : list or None optional (default=None)
Nodes to keep fixed at initial position.
iterations : int optional (default=50)
Maximum number of iterations taken
threshold: float optional (default = 1e-4)
Threshold for relative error in node position changes.
The iteration stops if the error is below this threshold.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number (default: 1)
Scale factor for positions. Not used unless `fixed is None`.
center : array-like or None
Coordinate pair around which to center the layout.
Not used unless `fixed is None`.
dim : int
Dimension of layout.
seed : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `seed` is the seed used by the random number generator,
if numpy.random.RandomState instance, `seed` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spring_layout(G)
# The same using longer but equivalent function name
>>> pos = nx.fruchterman_reingold_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
if fixed is not None:
nfixed = dict(zip(G, range(len(G))))
fixed = np.asarray([nfixed[v] for v in fixed])
if pos is not None:
# Determine size of existing domain to adjust initial positions
dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup)
if dom_size == 0:
dom_size = 1
pos_arr = seed.rand(len(G), dim) * dom_size + center
for i, n in enumerate(G):
if n in pos:
pos_arr[i] = np.asarray(pos[n])
else:
pos_arr = None
if len(G) == 0:
return {}
if len(G) == 1:
return {nx.utils.arbitrary_element(G.nodes()): center}
try:
# Sparse matrix
if len(G) < 500: # sparse solver for large graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype='f')
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _sparse_fruchterman_reingold(A, k, pos_arr, fixed,
iterations, threshold,
dim, seed)
except:
A = nx.to_numpy_array(G, weight=weight)
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _fruchterman_reingold(A, k, pos_arr, fixed, iterations,
threshold, dim, seed)
if fixed is None:
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
def graph_to_array(g):
if type(g) == nx.Graph:
g = nx.to_numpy_array(g)
elif type(g) == sp.sparse.csr_matrix:
g = g.toarray()
return g
def test_identity_graph_array(self):
"Conversion from graph to array to graph."
A = nx.to_numpy_array(self.G1)
self.identity_conversion(self.G1, A, nx.Graph())
def count_noiseless_subsystems(g: nx.Graph):
n = g.number_of_nodes()
m = nx.to_numpy_array(g) if g.number_of_edges() > 0 else np.zeros([n, n])
return count_noiseless_eigenvectors(m)
def test_identity_weighted_graph_array(self):
"""Conversion from weighted graph to array to weighted graph."""
A = nx.to_numpy_array(self.G3)
self.identity_conversion(self.G3, A, nx.Graph())
def fruchterman_reingold_layout(
G,
k=None,
pos=None,
fixed=None,
iterations=50,
threshold=1e-4,
weight="weight",
scale=1,
center=None,
dim=2,
seed=None,
):
"""Position nodes using Fruchterman-Reingold force-directed algorithm.
The algorithm simulates a force-directed representation of the network
treating edges as springs holding nodes close, while treating nodes
as repelling objects, sometimes called an anti-gravity force.
Simulation continues until the positions are close to an equilibrium.
There are some hard-coded values: minimal distance between
nodes (0.01) and "temperature" of 0.1 to ensure nodes don't fly away.
During the simulation, `k` helps determine the distance between nodes,
though `scale` and `center` determine the size and place after
rescaling occurs at the end of the simulation.
Fixing some nodes doesn't allow them to move in the simulation.
It also turns off the rescaling feature at the simulation's end.
In addition, setting `scale` to `None` turns off rescaling.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
k : float (default=None)
Optimal distance between nodes. If None the distance is set to
1/sqrt(n) where n is the number of nodes. Increase this value
to move nodes farther apart.
pos : dict or None optional (default=None)
Initial positions for nodes as a dictionary with node as keys
and values as a coordinate list or tuple. If None, then use
random initial positions.
fixed : list or None optional (default=None)
Nodes to keep fixed at initial position.
ValueError raised if `fixed` specified and `pos` not.
iterations : int optional (default=50)
Maximum number of iterations taken
threshold: float optional (default = 1e-4)
Threshold for relative error in node position changes.
The iteration stops if the error is below this threshold.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number or None (default: 1)
Scale factor for positions. Not used unless `fixed is None`.
If scale is None, no rescaling is performed.
center : array-like or None
Coordinate pair around which to center the layout.
Not used unless `fixed is None`.
dim : int
Dimension of layout.
seed : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `seed` is the seed used by the random number generator,
if numpy.random.RandomState instance, `seed` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spring_layout(G)
# The same using longer but equivalent function name
>>> pos = nx.fruchterman_reingold_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
if fixed is not None:
if pos is None:
raise ValueError("nodes are fixed without positions given")
for node in fixed:
if node not in pos:
raise ValueError("nodes are fixed without positions given")
nfixed = {node: i for i, node in enumerate(G)}
fixed = np.asarray([nfixed[node] for node in fixed])
if pos is not None:
# Determine size of existing domain to adjust initial positions
dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup)
if dom_size == 0:
dom_size = 1
pos_arr = seed.rand(len(G), dim) * dom_size + center
for i, n in enumerate(G):
if n in pos:
pos_arr[i] = np.asarray(pos[n])
else:
pos_arr = None
dom_size = 1
if len(G) == 0:
return {}
if len(G) == 1:
return {nx.utils.arbitrary_element(G.nodes()): center}
try:
# Sparse matrix
if len(G) < 500: # sparse solver for large graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype="f")
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _sparse_fruchterman_reingold(A, k, pos_arr, fixed, iterations,
threshold, dim, seed)
except ValueError:
A = nx.to_numpy_array(G, weight=weight)
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _fruchterman_reingold(A, k, pos_arr, fixed, iterations,
threshold, dim, seed)
if fixed is None and scale is not None:
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
def load_brazil_airport(feature_dim, initializer="None"):
'''
hardcoded for simplicity
'''
num_nodes = 131
num_feats = feature_dim if initializer != 'None' else 1433
train_size = int(num_nodes * 0.8)
test_size = num_nodes - train_size
if initializer == "1hot":
num_feats = num_nodes
feat_data = np.zeros((num_nodes, num_feats))
labels = np.empty((num_nodes, 1), dtype=np.int64)
node_map = {}
label_map = {}
label_node_list_map = {}
train_idx = []
test_idx = []
if initializer == "None":
with open("brazil-airports/labels-brazil-airports.txt") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
feat_data[i, :] = list(map(float, info[1:-1]))
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
else:
print("Initializing with", initializer)
with open("brazil-airports/labels-brazil-airports.txt") as fp:
fp.readline()
for i, line in enumerate(fp):
info = line.strip().split()
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
# set initializer method
if initializer == "1hot":
feat_data = np.eye(num_nodes)
elif initializer == "random_normal":
feat_data = np.random.normal(0, 1, (num_nodes, feature_dim))
elif initializer == "shared":
feat_data = np.ones((num_nodes, feature_dim))
elif initializer == "node_degree":
feat_data = np.zeros((num_nodes, 1))
elif initializer == "pagerank" or "eigen" in initializer:
G = nx.Graph()
G.add_nodes_from(node_map.values())
elif initializer == "deepwalk":
feat_data = extract_deepwalk_embeddings(
"brazil-airports/brazil-airports_{dim}.embeddings".format(
dim=feature_dim), node_map)
adj_lists = defaultdict(set)
with open("brazil-airports/brazil-airports.edgelist") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
paper1 = node_map[info[0]]
paper2 = node_map[info[1]]
adj_lists[paper1].add(paper2)
adj_lists[paper2].add(paper1)
if initializer == "pagerank" or "eigen" in initializer:
G.add_edge(paper1, paper2)
G.add_edge(paper2, paper1)
if "degree" in initializer:
# for k, v in adj_lists.items():
# feat_data[k] = len(v)
# convert to 1hot representation
node_degrees = [len(v) for v in adj_lists.values()]
if "degree_bucket" in initializer:
# simple hack for degree bucketization
boundaries = []
if initializer == "degree_bucket_range":
bucket_num = 10
bucket_size = int(80 / bucket_num)
boundaries = np.arange(bucket_size, 81, bucket_size)
elif initializer == "degree_bucket_distribution":
bucket_num = 10
bucket_size = int(100 / bucket_num)
for i in range(bucket_size, 101, bucket_size):
boundaries.append(
np.percentile(node_degrees, i, interpolation="higher"))
print("boundaries:", boundaries)
feat_data = np.zeros((num_nodes, bucket_num))
for k, v in adj_lists.items():
idx = torch.bucketize(len(v), torch.Tensor(boundaries))
feat_data[k, idx] = 1
assert np.count_nonzero(feat_data[k]) == 1
print(feat_data)
elif initializer == "node_degree":
max_degree = max(node_degrees)
feat_data = np.zeros((num_nodes, max_degree + 1))
for k, v in adj_lists.items():
feat_data[k, len(v)] = 1
elif initializer == "pagerank":
feat_data = np.zeros((num_nodes, feature_dim))
pagerank = nx.pagerank(G)
for k, v in pagerank.items():
feat_data[k, :] = v
elif "eigen" in initializer:
try:
if initializer == "eigen":
v = np.load("brazil-airports/brazil-airports_eigenvector.npy")
else:
v = np.load(
"brazil-airports/brazil-airports_eigenvector_degree_normalized.npy"
)
print(v.shape)
except:
adj_matrix = nx.to_numpy_array(G)
# normalize adjacency matrix with degree
if initializer == "eigen_norm":
sum_of_rows = adj_matrix.sum(axis=1)
adj_matrix = adj_matrix / sum_of_rows[:, None]
print("start computing eigen vectors")
w, v = LA.eig(adj_matrix)
indices = np.argsort(w)[::-1]
v = v.transpose()[indices]
# only save top 1000 eigenvectors
if initializer == "eigen":
np.save("brazil-airports/brazil-airports_eigenvector",
v[:1000])
else:
np.save(
"brazil-airports/brazil-airports_eigenvector_degree_normalized",
v[:1000])
# print(v)
feat_data = np.zeros((num_nodes, feature_dim))
# assert(feature_dim <= 1000)
for i in range(num_nodes):
for j in range(feature_dim):
feat_data[i, j] = v[j, i]
test_idx = []
for label, node_list in label_node_list_map.items():
node_list_size = len(node_list)
anchor = int(node_list_size * 0.8)
random.shuffle(node_list)
train_idx.extend(node_list[:anchor])
test_idx.extend(node_list[anchor:])
return feat_data, labels, train_idx, test_idx, adj_lists
def dist(
self,
G1,
G2,
normed=True,
kernel='normal',
hwhm=0.011775,
measure='jensen-shannon',
k=None,
which='LM',
):
"""Graph distances using different measure between the Laplacian
spectra of the two graphs
The spectra of both Laplacian matrices (normalized or not) is
computed. Then, the discrete spectra are convolved with a kernel to
produce continuous ones. Finally, these distribution are compared
using a metric.
The results dictionary also stores a 2-tuple of the underlying
adjacency matrices in the key `'adjacency_matrices'`, the Laplacian
matrices in `'laplacian_matrices'`, the eigenvalues of the
Laplacians in `'eigenvalues'`. If the networks being compared are
directed, the augmented adjacency matrices are calculated and
stored in `'augmented_adjacency_matrices'`.
Parameters
----------
G1, G2 (nx.Graph)
two networkx graphs to be compared.
normed (bool)
If True, uses the normalized laplacian matrix, otherwise the
raw laplacian matrix is used.
kernel (str)
kernel to obtain a continuous spectrum. Choices available are
'normal', 'lorentzian', or None. If None is chosen, the
discrete spectrum is used instead, and the measure is simply
the euclidean distance between the vector of eigenvalues for
each graph.
hwhm (float)
half-width at half-maximum for the kernel. The default value is
chosen such that the standard deviation for the normal
distribution is :math:`0.01`, as in reference [1]_. This option
is relevant only if kernel is not None.
measure (str)
metric between the two continuous spectra. Choices available
are 'jensen-shannon' or 'euclidean'. This option is relevant
only if kernel is not None.
k (int)
number of eigenvalues kept for the (discrete) spectrum, also
used to create the continuous spectrum. If None, all the
eigenvalues are used. k must be smaller (strictly) than the
size of both graphs.
which (str)
if k is not None, this option specifies the eigenvalues that
are kept. See the choices offered by
`scipy.sparse.linalg.eigsh`. The largest eigenvalues in
magnitude are kept by default.
Returns
-------
dist (float)
the distance between G1 and G2.
Notes
-----
The methods are usually applied to undirected (unweighted)
networks. We however relax this assumption using the same method
proposed for the Hamming-Ipsen-Mikhailov. See [2]_.
References
----------
.. [1] https://www.sciencedirect.com/science/article/pii/S0303264711001869.
.. [2] https://ieeexplore.ieee.org/abstract/document/7344816.
"""
adj1 = nx.to_numpy_array(G1)
adj2 = nx.to_numpy_array(G2)
self.results['adjacency_matrices'] = adj1, adj2
directed = nx.is_directed(G1) or nx.is_directed(G2)
if directed:
# create augmented adjacency matrices
N1 = len(G1)
N2 = len(G2)
null_mat1 = np.zeros((N1, N1))
null_mat2 = np.zeros((N2, N2))
adj1 = np.block([[null_mat1, adj1.T], [adj1, null_mat1]])
adj2 = np.block([[null_mat2, adj2.T], [adj2, null_mat2]])
self.results['augmented_adjacency_matrices'] = adj1, adj2
# get the laplacian matrices
lap1 = laplacian(adj1, normed=normed)
lap2 = laplacian(adj2, normed=normed)
self.results['laplacian_matrices'] = lap1, lap2
# get the eigenvalues of the laplacian matrices
if k is None:
ev1 = np.abs(eigvalsh(lap1))
ev2 = np.abs(eigvalsh(lap2))
else:
# transform the dense laplacian matrices to sparse representations
lap1 = csgraph_from_dense(lap1)
lap2 = csgraph_from_dense(lap2)
ev1 = np.abs(eigsh(lap1, k=k, which=which)[0])
ev2 = np.abs(eigsh(lap2, k=k, which=which)[0])
self.results['eigenvalues'] = ev1, ev2
if kernel is not None:
# define the proper support
a = 0
if normed:
b = 2
else:
b = np.inf
# create continuous spectra
density1 = _create_continuous_spectrum(ev1, kernel, hwhm, a, b)
density2 = _create_continuous_spectrum(ev2, kernel, hwhm, a, b)
# compare the spectra
dist = _spectra_comparison(density1, density2, a, b, measure)
self.results['dist'] = dist
else:
# euclidean distance between the two discrete spectra
dist = np.linalg.norm(ev1 - ev2)
self.results['dist'] = dist
return dist
def load_cora(feature_dim, initializer="None"):
num_nodes = 2708
num_feats = feature_dim if initializer != 'None' else 1433
num_classes = 7
train_size = num_classes * 20
if initializer == "1hot":
num_feats = num_nodes
feat_data = np.zeros((num_nodes, num_feats))
labels = np.empty((num_nodes, 1), dtype=np.int64)
node_map = {}
label_map = {}
label_node_list_map = {}
train_idx = []
test_idx = []
val_idx = []
if initializer == "None":
with open("cora/cora.content") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
feat_data[i, :] = list(map(float, info[1:-1]))
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
else:
print("Initializing with", initializer)
with open("cora/cora.content") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
node_map[info[0]] = i
if not info[-1] in label_map:
label_map[info[-1]] = len(label_map)
label_node_list_map[len(label_map) - 1] = []
labels[i] = label_map[info[-1]]
label_node_list_map[labels[i][0]].append(i)
# set initializer method
if initializer == "1hot":
feat_data = np.eye(num_nodes)
elif initializer == "random_normal":
feat_data = np.random.normal(0, 1, (num_nodes, feature_dim))
elif initializer == "shared":
feat_data = np.ones((num_nodes, feature_dim))
elif initializer == "node_degree":
feat_data = np.zeros((num_nodes, 1))
elif initializer == "pagerank" or initializer == "eigen":
G = nx.Graph()
G.add_nodes_from(node_map.values())
elif initializer == "deepwalk":
feat_data = extract_deepwalk_embeddings(
"cora/cora_{dim}.embeddings".format(dim=feature_dim), node_map)
adj_lists = defaultdict(set)
with open("cora/cora.cites") as fp:
for i, line in enumerate(fp):
info = line.strip().split()
paper1 = node_map[info[0]]
paper2 = node_map[info[1]]
adj_lists[paper1].add(paper2)
adj_lists[paper2].add(paper1)
if initializer == "pagerank" or initializer == "eigen":
G.add_edge(paper1, paper2)
G.add_edge(paper2, paper1)
if initializer == "node_degree":
# convert to 1hot representation
node_degrees = [len(v) for v in adj_lists.values()]
max_degree = max(node_degrees)
feat_data = np.zeros((num_nodes, max_degree + 1))
for k, v in adj_lists.items():
feat_data[k, len(v)] = 1
elif initializer == "pagerank":
feat_data = np.zeros((num_nodes, feature_dim))
pagerank = nx.pagerank(G)
for k, v in pagerank.items():
feat_data[k, :] = v
elif "eigen" in initializer:
try:
if initializer == "eigen":
v = np.load("cora/cora_eigenvector.npy")
else:
v = np.load("cora/cora_eigenvector_degree_normalized.npy")
print(v.shape)
except:
adj_matrix = nx.to_numpy_array(G)
# normalize adjacency matrix with degree
if initializer == "eigen_norm":
sum_of_rows = adj_matrix.sum(axis=1)
adj_matrix = adj_matrix / sum_of_rows[:, None]
print("start computing eigen vectors")
w, v = LA.eig(adj_matrix)
indices = np.argsort(w)[::-1]
v = v.transpose()[indices]
# only save top 1000 eigenvectors
np.save("cora/cora_eigenvector", v[:2000])
if initializer == "eigen":
np.save("cora/cora_eigenvector", v[:1000])
else:
np.save("cora/cora_eigenvector_degree_normalized", v[:1000])
# print(v)
feat_data = np.zeros((num_nodes, feature_dim))
for i in range(num_nodes):
for j in range(feature_dim):
feat_data[i, j] = v[j, i]
for label, node_list in label_node_list_map.items():
random.shuffle(node_list)
train_idx.extend(node_list[:20])
anchor = 20 + int(500 / num_classes)
val_idx.extend(node_list[20:anchor])
test_idx.extend(node_list[anchor:])
return feat_data, labels, train_idx, test_idx, val_idx, adj_lists
def authority_matrix(G, nodelist=None):
"""Returns the HITS authority matrix."""
M = nx.to_numpy_array(G, nodelist=nodelist)
return M.T @ M
def simrank_similarity_numpy(G, source=None, target=None, importance_factor=0.9,
max_iterations=100, tolerance=1e-4):
"""Calculate SimRank of nodes in ``G`` using matrices with ``numpy``.
The SimRank algorithm for determining node similarity is defined in
[1]_.
Parameters
----------
G : NetworkX graph
A NetworkX graph
source : node
If this is specified, the returned dictionary maps each node
``v`` in the graph to the similarity between ``source`` and
``v``.
target : node
If both ``source`` and ``target`` are specified, the similarity
value between ``source`` and ``target`` is returned. If
``target`` is specified but ``source`` is not, this argument is
ignored.
importance_factor : float
The relative importance of indirect neighbors with respect to
direct neighbors.
max_iterations : integer
Maximum number of iterations.
tolerance : float
Error tolerance used to check convergence. When an iteration of
the algorithm finds that no similarity value changes more than
this amount, the algorithm halts.
Returns
-------
similarity : dictionary or float
If ``source`` and ``target`` are both ``None``, this returns a
dictionary of dictionaries, where keys are node pairs and value
are similarity of the pair of nodes.
If ``source`` is not ``None`` but ``target`` is, this returns a
dictionary mapping node to the similarity of ``source`` and that
node.
If neither ``source`` nor ``target`` is ``None``, this returns
the similarity value for the given pair of nodes.
Examples
--------
>>> import networkx as nx
>>> from numpy import array
>>> G = nx.cycle_graph(4)
>>> sim = nx.simrank_similarity_numpy(G)
References
----------
.. [1] G. Jeh and J. Widom.
"SimRank: a measure of structural-context similarity",
In KDD'02: Proceedings of the Eighth ACM SIGKDD
International Conference on Knowledge Discovery and Data Mining,
pp. 538--543. ACM Press, 2002.
"""
# This algorithm follows roughly
#
# S = max{C * (A.T * S * A), I}
#
# where C is the importance factor, A is the column normalized
# adjacency matrix, and I is the identity matrix.
import numpy as np
adjacency_matrix = nx.to_numpy_array(G)
# column-normalize the ``adjacency_matrix``
adjacency_matrix /= adjacency_matrix.sum(axis=0)
newsim = np.eye(adjacency_matrix.shape[0], dtype=np.float64)
for _ in range(max_iterations):
prevsim = np.copy(newsim)
newsim = importance_factor * np.matmul(
np.matmul(adjacency_matrix.T, prevsim), adjacency_matrix)
np.fill_diagonal(newsim, 1.0)
if np.allclose(prevsim, newsim, atol=tolerance):
break
if source is not None and target is not None:
return newsim[source, target]
if source is not None:
return newsim[source]
return newsim
def recalc_layout_force(self):
"""calculate new change_array"""
logging.info('force recalculating starting')
# get node array
# self.base_pos_ar = np.array([(self.g.nodes[i]['x'],self.g.nodes[i]['y']) for i in self.g.nodes])
# base_pos_ar = np.array([(g.nodes[i]['x'],g.nodes[i]['y']) for i in g.nodes])
pos_nds = np.copy(self.base_pos_ar)
# pos_nds = pos_nds.astype('float64')
pos_nds = pos_nds.astype('float32')
A = nx.to_numpy_array(self.g)
At = A.T
A = A + At
np.clip(A, 0, 1, out = A)
# A = A.astype('float')
# get corner points pos
sqs = []
for n in self.g.nodes():
logging.info(['node', n])
sqx = rect_points([self.g.nodes[n]['x'], self.g.nodes[n]['y'],
self.g.nodes[n]['width'], self.g.nodes[n]['height']])
sqs.append(sqx)
pos = np.concatenate(sqs)
pos = pos.astype('float32')
row_order = get_reorder_order_sliced(len(self.g.nodes))
nbr_nds = A.shape[0]
nbr_pts = pos.shape[0]
# self.dim_ar = np.array([[self.g.nodes[i]['width'], self.g.nodes[i]['height']] for i in self.g.nodes])
dim_ar2 = self.dim_ar.astype('float32')
# pythran_res = pythran_itrtr_cbn(pos, pos_nds, A, row_order, dim_ar2, self.t, self.def_itr,
# self.rep_nd_brd_start, self.k, self.height*1.0, self.width*1.0, grav_multiplier)
# pos_nds = pythran_res[0]
# ctr = pythran_res[2]
# construct objects for seeing which nodes are edge label nodes
elbl_pos_list = []
elbl_cnct_nds = []
c = 0
for v in self.g.nodes:
if self.g.nodes[v]['nd_tp'] == 'lbl':
# g.nodes[v]['e_lbl'] = 1
logging.info(["v: ", v, ", c: ", c])
elbl_pos_list.append(c)
cnct_nodes = list(self.g.predecessors(v)) + list(self.g.successors(v))
logging.info(["connected nodes: ", cnct_nodes])
elbl_cnct_nds.append([self.vd[cnct_nodes[0]], self.vd[cnct_nodes[1]]])
c +=1
elbl_pos_list = np.array(elbl_pos_list)
elbl_cnct_nds = np.array(elbl_cnct_nds)
logging.info(["elbl_pos_list:\n", elbl_pos_list])
logging.info(["elbl_cnct_nds:\n", elbl_cnct_nds])
t1 = time()
ctr = 0
grav_multiplier = 5.0
logging.info(['pos_nds:\n', pos_nds])
pos_nds = frucht(pos_nds, dim_ar2, self.k*1.0, A, self.width*1.0, self.height*1.0, self.t,
500, self.def_itr, self.rep_nd_brd_start,
elbl_pos_list, elbl_cnct_nds, 1.0
)
logging.info(['pos_nds:\n', pos_nds])
ctr = 0
t2 = time()
logging.info('calculated layout in ' + str(round(t2-t1,4)) + ' seconds with ' + str(ctr) + ' iterations')
# base_pos_ar = np.array([(g.nodes[i]['x'],g.nodes[i]['y']) for i in g.nodes])
# self.goal_vp = sfdp_layout(self.g, K=0.5, pos=self.pos_vp, **set_dict)
# self.goal_vp = fruchterman_reingold_layout(self.g, pos = self.pos_vp)
self.chng_ar = (pos_nds - self.base_pos_ar)/self.step
# re-assign back to graph, just do once at end
for i in zip(self.g.nodes, pos_nds):
self.g.nodes[i[0]]['x'] = i[1][0]
self.g.nodes[i[0]]['y'] = i[1][1]
# print("base_pos_ar: ", self.base_pos_ar)
logging.info('force recalculating done')