def main():
parser = ArgumentParser(description="GraphZoom")
parser.add_argument("-d", "--dataset", type=str, default="cora", \
help="input dataset")
parser.add_argument("-o", "--coarse", type=str, default="simple", \
help="choose either simple_coarse or lamg_coarse, [simple, lamg]")
parser.add_argument("-c", "--mcr_dir", type=str, default="/opt/matlab/R2018A/", \
help="directory of matlab compiler runtime (only required by lamg_coarsen)")
parser.add_argument("-s", "--search_ratio", type=int, default=12, \
help="control the search space in graph fusion process (only required by lamg_coarsen)")
parser.add_argument("-r", "--reduce_ratio", type=int, default=2, \
help="control graph coarsening levels (only required by lamg_coarsen)")
parser.add_argument("-v", "--level", type=int, default=1, \
help="number of coarsening levels (only required by simple_coarsen)")
parser.add_argument("-n", "--num_neighs", type=int, default=2, \
help="control k-nearest neighbors in graph fusion process")
parser.add_argument("-l", "--lda", type=float, default=0.1, \
help="control self loop in adjacency matrix")
parser.add_argument("-e", "--embed_path", type=str, default="embed_results/embeddings.npy", \
help="path of embedding result")
parser.add_argument("-m", "--embed_method", type=str, default="deepwalk", \
help="[deepwalk, node2vec, graphsage]")
parser.add_argument("-f", "--fusion", default=True, action="store_false", \
help="whether use graph fusion")
parser.add_argument("-p", "--power", default=False, action="store_true", \
help="Strong power of graph filter, set True to enhance filter power")
parser.add_argument("-g", "--sage_model", type=str, default="mean", \
help="aggregation function in graphsage")
parser.add_argument("-w", "--sage_weighted", default=True, action="store_false", \
help="whether consider weighted reduced graph")
args = parser.parse_args()
dataset = args.dataset
feature_path = "dataset/{}/{}-feats.npy".format(dataset, dataset)
fusion_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
reduce_results = "reduction_results/"
mapping_path = "{}Mapping.mtx".format(reduce_results)
if args.fusion:
coarsen_input_path = "dataset/{}/fused_{}.mtx".format(dataset, dataset)
else:
coarsen_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
######Load Data######
print("%%%%%% Loading Graph Data %%%%%%")
laplacian = json2mtx(dataset)
## whether node features are required
if args.fusion or args.embed_method == "graphsage":
feature = np.load(feature_path)
######Graph Fusion######
if args.fusion:
print("%%%%%% Starting Graph Fusion %%%%%%")
fusion_start = time.process_time()
laplacian = graph_fusion(laplacian, feature, args.num_neighs, args.mcr_dir, args.coarse,\
fusion_input_path, args.search_ratio, reduce_results, mapping_path, dataset)
fusion_time = time.process_time() - fusion_start
######Graph Reduction######
print("%%%%%% Starting Graph Reduction %%%%%%")
reduce_start = time.process_time()
if args.coarse == "simple":
G, projections, laplacians, level = sim_coarse(laplacian, args.level)
reduce_time = time.process_time() - reduce_start
elif args.coarse == "lamg":
os.system('./run_coarsening.sh {} {} {} n {}'.format(args.mcr_dir, \
coarsen_input_path, args.reduce_ratio, reduce_results))
reduce_time = read_time("{}CPUtime.txt".format(reduce_results))
G = mtx2graph("{}Gs.mtx".format(reduce_results))
level = read_levels("{}NumLevels.txt".format(reduce_results))
projections, laplacians = construct_proj_laplacian(
laplacian, level, reduce_results)
else:
raise NotImplementedError
######Embed Reduced Graph######
print("%%%%%% Starting Graph Embedding %%%%%%")
if args.embed_method == "deepwalk":
embed_start = time.process_time()
embeddings = deepwalk(G)
elif args.embed_method == "node2vec":
embed_start = time.process_time()
embeddings = node2vec(G)
elif args.embed_method == "graphsage":
from embed_methods.graphsage.graphsage import graphsage
nx.set_node_attributes(G, False, "test")
nx.set_node_attributes(G, False, "val")
## obtain mapping operator
if args.coarse == "lamg":
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
else:
mapping = identity(feature.shape[0])
for p in projections:
mapping = mapping @ p
mapping = normalize(mapping, norm='l1', axis=1).transpose()
## control iterations for training
coarse_ratio = mapping.shape[1] / mapping.shape[0]
## map node feats to the coarse graph
feats = mapping @ feature
embed_start = time.process_time()
embeddings = graphsage(G, feats, args.sage_model, args.sage_weighted,
int(1000 / coarse_ratio))
embed_time = time.process_time() - embed_start
######Refinement######
print("%%%%%% Starting Graph Refinement %%%%%%")
refine_start = time.process_time()
embeddings = refinement(level, projections, laplacians, embeddings,
args.lda, args.power)
refine_time = time.process_time() - refine_start
######Save Embeddings######
np.save(args.embed_path, embeddings)
######Evaluation######
lr("dataset/{}/".format(dataset), args.embed_path, dataset)
######Report timing information######
print("%%%%%% CPU time %%%%%%")
if args.fusion:
total_time = fusion_time + reduce_time + embed_time + refine_time
print(f"Graph Fusion Time: {fusion_time:.3f}")
else:
total_time = reduce_time + embed_time + refine_time
print("Graph Fusion Time: 0")
print(f"Graph Reduction Time: {reduce_time:.3f}")
print(f"Graph Embedding Time: {embed_time:.3f}")
print(f"Graph Refinement Time: {refine_time:.3f}")
print(
f"Total Time = Fusion_time + Reduction_time + Embedding_time + Refinement_time = {total_time:.3f}"
)
elif args.embed_method == "node2vec":
embed_start = time.process_time()
embeddings = node2vec(G)
embed_end = time.process_time()
elif args.embed_method == "graphsage":
from embed_methods.graphsage.graphsage import graphsage
nx.set_node_attributes(G, False, "test")
nx.set_node_attributes(G, False, "val")
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
feats = mapping @ feature
embed_start = time.process_time()
embeddings = graphsage(G, feats, args.sage_model, args.sage_weighted, int(10000 / args.reduce_ratio))
embed_end = time.process_time()
elif args.embed_method == "dgi":
from embed_methods.dgi.execute import dgi
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
feats = mapping @ feature
embed_start = time.process_time()
embeddings = dgi(G, feats)
embed_end = time.process_time()
embed_time = embed_end - embed_start
######Load Refinement Data######
levels = read_levels(level_path)
def main():
parser = ArgumentParser(description="ne")
parser.add_argument("-d", "--dataset", type=str, default="cora", \
help="input dataset")
parser.add_argument("-o", "--coarse", type=str, default="simple", \
help="choose either simple_coarse or lamg_coarse, [simple, lamg]")
parser.add_argument("-c", "--mcr_dir", type=str, default="/opt/matlab/R2018A/", \
help="directory of matlab compiler runtime (only required by lamg_coarsen)")
parser.add_argument("-s", "--search_ratio", type=int, default=12, \
help="control the search space in graph fusion process (only required by lamg_coarsen)")
parser.add_argument("-r", "--reduce_ratio", type=int, default=2, \
help="control graph coarsening levels (only required by lamg_coarsen)")
parser.add_argument("-v", "--level", type=int, default=1, \
help="number of coarsening levels (only required by simple_coarsen)")
parser.add_argument("-n", "--num_neighs", type=int, default=2, \
help="control k-nearest neighbors in graph fusion process")
parser.add_argument("-l", "--lda", type=float, default=0.1, \
help="control self loop in adjacency matrix")
parser.add_argument("-e", "--embed_path", type=str, default="embed_results/embeddings_palone_deepwalk.npy", \
help="path of embedding result")
parser.add_argument("-m", "--embed_method", type=str, default="deepwalk", \
help="[deepwalk, node2vec, graphsage]")
parser.add_argument("-f", "--fusion", default=True, action="store_false", \
help="whether use graph fusion")
parser.add_argument("-p", "--power", default=False, action="store_true", \
help="Strong power of graph filter, set True to enhance filter power")
parser.add_argument("-g", "--sage_model", type=str, default="mean", \
help="aggregation function in graphsage")
parser.add_argument("-w", "--sage_weighted", default=True, action="store_false", \
help="whether consider weighted reduced graph")
args = parser.parse_args()
dataset = args.dataset
feature_path = "dataset/{}/{}-feats.npy".format(dataset, dataset)
fusion_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
reduce_results = "reduction_results/"
mapping_path = "{}Mapping.mtx".format(reduce_results)
if args.fusion:
coarsen_input_path = "dataset/{}/fused_{}.mtx".format(dataset, dataset)
else:
coarsen_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
######Load Data######
print("%%%%%% Loading Graph Data %%%%%%")
if args.dataset == "ogb":
d_name = "ogbl-ppa"
from ogb.linkproppred import LinkPropPredDataset
dataset = LinkPropPredDataset(name=d_name)
print(dataset)
print(dataset[0])
split_edge = dataset.get_edge_split()
print(split_edge)
# train_edge, valid_edge, test_edge = split_edge["train"], split_edge["valid"], split_edge["test"]
graph = dataset[0] # graph: library-agnostic graph object
print(graph['edge_index'].shape)
print(graph['edge_feat'])
print(graph['node_feat'])
# print((np.array(graph['node_feat']) == 0.0).all())
graph['directed'] = False
print(graph)
graph_nodes = [i for i in range(0, graph['num_nodes'])]
G = nx.Graph()
G.add_nodes_from(graph_nodes)
G.add_edges_from(graph['edge_index'].T)
# nx.draw(G, with_labels=True)
print(G.nodes)
# plt.show()
laplacian = laplacian_matrix(G)
print(laplacian)
else:
path = "dataset/ppi/ppi.mtx"
G = mtx2graph(path)
laplacian, edges = json2mtx(dataset)
## whether node features are required
if args.fusion or args.embed_method == "graphsage":
if args.dataset == 'ogb':
feature = graph['node_feat']
else:
feature = np.load(feature_path)
# print(feature[1][0])
######Embed Reduced Graph######
print("%%%%%% Starting Graph Embedding %%%%%%")
if args.embed_method == "deepwalk":
embed_start = time.process_time()
embeddings = deepwalk(G)
elif args.embed_method == "node2vec":
embed_start = time.process_time()
embeddings = node2vec(G)
elif args.embed_method == "graphsage":
from embed_methods.graphsage.graphsage import graphsage
nx.set_node_attributes(G, False, "test")
nx.set_node_attributes(G, False, "val")
## obtain mapping operator
if args.coarse == "lamg":
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
else:
mapping = identity(feature.shape[0])
for p in projections:
mapping = mapping @ p
mapping = normalize(mapping, norm='l1', axis=1).transpose()
## control iterations for training
coarse_ratio = mapping.shape[1] / mapping.shape[0]
## map node feats to the coarse graph
feats = mapping @ feature
embed_start = time.process_time()
embeddings = graphsage(G, feats, args.sage_model, args.sage_weighted,
int(1000 / coarse_ratio))
embed_time = time.process_time() - embed_start
######Save Embeddings######
np.save(args.embed_path, embeddings)
######Evaluation######
print("%%%%%% Starting Evaluation %%%%%%")
# link prediction
embeds = np.load(args.embed_path)
'''
if args.dataset == "ogb":
acc, pre, sen, mcc, auc = linkprediction_ogb(split_edge, embeds)
else:
acc, pre, sen, mcc, auc = linkprediction(edges, embeds, dataset)'''
print("Running regression..")
# node prediction
# run_regression(np.array(train_embeds), np.array(train_labels), np.array(test_embeds), np.array(test_labels))
# lr("dataset/{}/".format(dataset), args.embed_path, dataset)
######Report timing information######å
print("%%%%%% CPU time %%%%%%")
if args.fusion:
total_time = embed_time
print(f"Graph Fusion Time:")
else:
total_time = embed_time
print("Graph Fusion Time: 0")
print(f"Graph Embedding Time: {embed_time:.3f}")
print(f"Total Time = Embedding_time = {total_time:.3f}")
def main():
parser = ArgumentParser(description="GraphZoom")
parser.add_argument("-d",
"--dataset",
type=str,
default="cora",
help="input dataset")
parser.add_argument("-c",
"--mcr_dir",
type=str,
default="/opt/matlab/R2018A/",
help="directory of matlab compiler runtime")
parser.add_argument(
"-s",
"--search_ratio",
type=int,
default=12,
help="control the search space in graph fusion process")
parser.add_argument("-k",
"--kpower",
type=int,
default=2,
help="control the graph filter power")
parser.add_argument("-r",
"--reduce_ratio",
type=int,
default=2,
help="control graph coarsening levels")
parser.add_argument(
"-n",
"--num_neighs",
type=int,
default=2,
help="control k-nearest neighbors in graph fusion process")
parser.add_argument("-l",
"--lda",
type=float,
default=0.1,
help="control self loop in adjacency matrix")
parser.add_argument("-e",
"--embed_path",
type=str,
default="embed_results/embeddings.npy",
help="path of embedding result")
parser.add_argument("-m",
"--embed_method",
type=str,
default="dgi",
help="[deepwalk, node2vec, graphsage, dgi]")
parser.add_argument("-f",
"--fusion",
default=False,
action="store_true",
help="whether use graph fusion")
parser.add_argument(
"-p",
"--power",
default=False,
action="store_true",
help="Strong power of graph filter, set True to enhance filter power")
parser.add_argument("-g",
"--sage_model",
type=str,
default="mean",
help="aggregation function in graphsage")
parser.add_argument("-w",
"--sage_weighted",
default=True,
action="store_false",
help="whether consider weighted reduced graph")
args = parser.parse_args()
dataset = args.dataset
mcr_dir = args.mcr_dir
search_ratio = args.search_ratio
num_neighs = args.num_neighs
ratio = args.reduce_ratio
lda = args.lda
mapping_path = "reduction_results/Mapping.mtx"
feature_path = "dataset/{}/{}-feats.npy".format(dataset, dataset)
fusion_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
fusion_output_dir = "reduction_results/"
output_dir = "reduction_results/"
mtx_path = "reduction_results/Gs.mtx"
level_path = "reduction_results/NumLevels.txt"
proj_dir = "reduction_results"
save_dir = args.embed_path
eval_dataset = "dataset/{}/".format(dataset)
reduce_method = "graphzoom"
cputime_path = "reduction_results/CPUtime.txt"
if args.fusion:
input_path = "dataset/{}/fused_{}.mtx".format(dataset, dataset)
else:
input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
######Load Data######
print("%%%%%% Loading Graph Data %%%%%%")
if os.path.exists(fusion_input_path):
laplacian = mmread(fusion_input_path)
else:
laplacian = json2mtx(dataset)
if args.fusion or args.embed_method == "graphsage" or args.embed_method == "dgi": ##whether feature is needed
feature = np.load(feature_path)
######Graph Fusion######
if args.fusion:
print("%%%%%% Starting Graph Fusion %%%%%%")
fusion_start = time.process_time()
laplacian = graph_fusion(laplacian, feature, num_neighs, mcr_dir,
fusion_input_path, search_ratio,
fusion_output_dir, mapping_path, dataset)
fusion_end = time.process_time()
fusion_time = fusion_end - fusion_start
######Graph Reduction######
print("%%%%%% Starting Graph Reduction %%%%%%")
os.system('./run_coarsening.sh {} {} {} n {}'.format(
mcr_dir, input_path, ratio, output_dir))
reduce_time = read_time(cputime_path)
######Embed Reduced Graph######
G = mtx2graph(mtx_path)
print("%%%%%% Starting Graph Embedding %%%%%%")
if args.embed_method == "deepwalk":
embed_start = time.process_time()
embeddings = deepwalk(G)
embed_end = time.process_time()
elif args.embed_method == "node2vec":
embed_start = time.process_time()
embeddings = node2vec(G)
embed_end = time.process_time()
elif args.embed_method == "graphsage":
from embed_methods.graphsage.graphsage import graphsage
nx.set_node_attributes(G, False, "test")
nx.set_node_attributes(G, False, "val")
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
feats = mapping @ feature
embed_start = time.process_time()
embeddings = graphsage(G, feats, args.sage_model, args.sage_weighted,
int(10000 / args.reduce_ratio))
embed_end = time.process_time()
elif args.embed_method == "dgi":
from embed_methods.dgi.execute import dgi
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
feats = mapping @ feature
embed_start = time.process_time()
embeddings = dgi(G, feats)
embed_end = time.process_time()
embed_time = embed_end - embed_start
######Load Refinement Data######
levels = read_levels(level_path)
projections, coarse_laplacian = construct_proj_laplacian(
laplacian, levels, proj_dir)
######Refinement######
print("%%%%%% Starting Graph Refinement %%%%%%")
feat = normalize(projections[0], norm='l1', axis=1) @ feature
refine_start = time.process_time()
embeddings = refinement(levels, projections, coarse_laplacian, embeddings,
lda, args.power, args.kpower, feat)
refine_end = time.process_time()
refine_time = refine_end - refine_start
######Save Embeddings######
np.save(save_dir, embeddings)
######Evaluation######
lr(eval_dataset, save_dir, dataset)
######Report timing information######
print("%%%%%% Single CPU time %%%%%%")
if args.fusion:
total_time = fusion_time + reduce_time + embed_time + refine_time
time_info = [
fusion_time, reduce_time, embed_time, refine_time, total_time
]
print("Graph Fusion Time: {}".format(fusion_time))
else:
total_time = reduce_time + embed_time + refine_time
time_info = [reduce_time, embed_time, refine_time, total_time]
print("Graph Reduction Time: {}".format(reduce_time))
print("Graph Embedding Time: {}".format(embed_time))
print("Graph Refinement Time: {}".format(refine_time))
print(
"Total Time = Fusion_time + Reduction_time + Embedding_time + Refinement_time = {}"
.format(total_time))
def main():
parser = ArgumentParser(description="GraphZoom")
parser.add_argument("-d",
"--dataset",
type=str,
default="cora",
help="input dataset")
parser.add_argument("-c",
"--mcr_dir",
type=str,
default="/usr/local/MATLAB/MATLAB_Runtime/v94",
help="directory of matlab compiler runtime")
parser.add_argument(
"-s",
"--search_ratio",
type=int,
default=12,
help="control the search space in graph fusion process")
parser.add_argument(
"-r",
"--reduce_ratio",
type=int,
default=2, # ? difference between level?
help="control graph coarsening levels")
parser.add_argument(
"-n",
"--num_neighs",
type=int,
default=2,
help="control k-nearest neighbors in graph fusion process")
parser.add_argument("-l",
"--lda",
type=float,
default=0.1,
help="control self loop in adjacency matrix")
parser.add_argument("-e",
"--embed_path",
type=str,
default="embed_results/",
help="path of embedding result")
parser.add_argument("-m",
"--embed_method",
type=str,
default="deepwalk",
help="[deepwalk, node2vec, graphsage]")
parser.add_argument("-pre", "--prefix", type=str, default="")
parser.add_argument("-pj",
"--proj",
type=str,
default='fusion',
help="projection matrix type")
parser.add_argument("-emb_arch", "--emb_arch", default='GCN')
parser.add_argument(
"-p",
"--power",
default=False,
action="store_true",
help="Strong power of graph filter, set True to enhance filter power")
parser.add_argument("-g",
"--sage_model",
type=str,
default="mean",
help="aggregation function in graphsage")
parser.add_argument("-w",
"--sage_weighted",
default=True,
action="store_false",
help="whether consider weighted reduced graph")
parser.add_argument("-el", "--embed_level", type=int, default=1)
args = parser.parse_args()
dataset = args.dataset
# feature_path = "{}/dataset/{}/{}-feats.npy".format(args.prefix, dataset, dataset)
fusion_input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
proj_matrix_type = args.proj
reduce_results = f"reduction_results/{dataset}/{proj_matrix_type}/"
coarsen_flag = True
if not Path(reduce_results).exists():
Path(reduce_results).mkdir(parents=True)
else:
coarsen_flag = False
print('skip fusion & coarsen')
mapping_path = "{}Mapping.mtx".format(reduce_results)
if args.proj in ('fusion'):
input_path = "dataset/{}/fused_{}.mtx".format(dataset, dataset)
else:
input_path = "dataset/{}/{}.mtx".format(dataset, dataset)
print(f'coarse_input_path: {input_path}')
######Load Data######
print("%%%%%% Loading Graph Data %%%%%%")
laplacian, feature = load_dataset(dataset, args.prefix)
# if args.fusion or args.embed_method == "graphsage": # whether feature is needed
# feature = np.load(feature_path)
######Graph Fusion######
fusion_time, reduce_time = 0, 0
if Path(input_path).exists():
laplacian = mmread(input_path)
print('load previous dataset laplacian')
else:
print("%%%%%% Starting Graph Fusion %%%%%%")
print('start fusion calculation')
fusion_start = time.process_time()
laplacian = graph_fusion(
laplacian, feature, args.num_neighs, args.mcr_dir,
fusion_input_path, args.search_ratio, reduce_results, mapping_path,
dataset) # load original mapping matrix, fusion on it
fusion_time = time.process_time() - fusion_start
print("Graph Fusion Time: {}".format(fusion_time))
######Graph Reduction######
# ! ignore fusion coarsen
if args.proj not in ['border', 'one_hot']:
print("%%%%%% Starting Graph Reduction %%%%%%")
os.system('./run_coarsening.sh {} {} {} n {}'.format(
args.mcr_dir, input_path, args.reduce_ratio, reduce_results))
reduce_time = read_time("{}CPUtime.txt".format(reduce_results))
else:
print(f'load original projections')
######Embed Reduced Graph######
G = mtx2graph("{}Gs.mtx".format(reduce_results))
# G = mtx2graph("dataset/{}/{}_ori.mtx".format(dataset, dataset))
levels = read_levels("{}NumLevels.txt".format(reduce_results))
print("%%%%%% Starting Graph Embedding %%%%%%")
print(G.number_of_edges(), G.number_of_nodes())
embed_start = time.process_time()
if args.embed_method == "deepwalk":
embeddings = deepwalk(G)
elif args.embed_method == "node2vec":
embeddings = node2vec(G)
elif args.embed_method == "graphsage":
from embed_methods.graphsage.graphsage import graphsage
nx.set_node_attributes(G, False, "test")
nx.set_node_attributes(G, False, "val")
mapping = normalize(mtx2matrix(mapping_path), norm='l1', axis=1)
feats = mapping @ feature
embeddings = graphsage(G, feats, args.sage_model, args.sage_weighted,
int(1000 / args.reduce_ratio))
elif args.embed_method == 'ft':
emb_path = f'../embeddings/{args.emb_arch}_{args.dataset}_emb_level_{levels}_mask.npy'
print(f'emb_path: {emb_path}')
# embeddings = np.load(f'{prefix}/{args.dataset}_emb_level_1.npy')
embeddings = np.load(emb_path)
embed_time = time.process_time() - embed_start
######Load Refinement Data######
# print(embeddings.shape) # corase_nodes * 128
projections, coarse_laplacian = construct_proj_laplacian(
laplacian, levels, reduce_results)
######Refinement######
print("%%%%%% Starting Graph Refinement %%%%%%")
refine_start = time.process_time()
embeddings = refinement(levels, projections, coarse_laplacian, embeddings,
args.lda, args.power)
refine_time = time.process_time() - refine_start
######Save Embeddings######
embed_path = f'{args.embed_path}/{args.dataset}_level_{levels}.npy'
print(f'embed_path: {embed_path}')
np.save(embed_path, embeddings) #! FK
######Evaluation######
if args.prefix != '':
lr("{}/dataset/{}/".format(args.prefix, dataset), embed_path, dataset)
else:
lr("dataset/{}/".format(dataset), embed_path, dataset)
######Report timing information######
print("%%%%%% Single CPU time %%%%%%")
if coarsen_flag:
total_time = fusion_time + reduce_time + embed_time + refine_time
print("Graph Fusion Time: {}".format(fusion_time))
else:
total_time = reduce_time + embed_time + refine_time
print("Graph Fusion Time: 0")
print("Graph Reduction Time: {}".format(reduce_time))
print("Graph Embedding Time: {:.3f} Mins".format(embed_time / 60))
print("Graph Refinement Time: {}".format(refine_time))
print(
"Total Time = Fusion_time + Reduction_time + Embedding_time + Refinement_time = {}"
.format(total_time))