def smallworldness(network, rep=1000):
g = network.g.copy()
#logger.info(g.summary())
# there is no point to consider a disconnected graph ( the average path length means nothing)
g = ResearchCollaborationNetwork.largest_component(g)
n = len(g.vs)
m = len(g.es)
p = float(m) * 2 / (n * (n - 1))
# sharp threshold: define the connectedness of a ER graph http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model
c = float((np.exp(1) + 1)) * np.log(n) / n
logger.info(
"Small-world-ness measure: %d iterations; Erdos_Renyi: p = %f (%d/%d), n = %d, np = %f, (1 + e) * (ln n / n) = %f"
% (rep, p, m, (n * (n - 1)) / 2, n, n * p, c))
ss = []
for bb in range(rep):
rg = igraph.Graph.Erdos_Renyi(n, p, directed=False, loops=False)
s = smallworldness_measure(g, rg)
ss.append(s)
mean_s = np.mean(ss)
return mean_s, ss
def centrality_leaders(budgetYears):
network = load_network_for(budgetYears)
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
topK = 10
candidates, rankings = cl.centrality_leaders(g)
ordered_list = []
for r in range(len(rankings))[:topK]:
#logger.info('tier: %d'%r)
for i in list(rankings[r]):
node_name = g.vs[candidates[i]]['name']
ordered_list.append(node_name)
# set the node's centrality_leader attribute, the higher the better
g.vs[candidates[i]]['centrality_leader'] = topK + 1 - r
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
filename = '%s/figures/%s-%s-centrality-leaders.png' % (root_folder(), startBudgetYear, endBudgetYear)
draw(g, filename)
logger.info(ordered_list)
def smallworldness(network, rep = 1000):
g = network.g.copy()
#logger.info(g.summary())
# there is no point to consider a disconnected graph ( the average path length means nothing)
g = ResearchCollaborationNetwork.largest_component(g)
n = len(g.vs)
m = len(g.es)
p = float(m) * 2 /(n*(n-1))
# sharp threshold: define the connectedness of a ER graph http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model
c = float((np.exp(1) + 1)) * np.log(n) / n
logger.info("Small-world-ness measure: %d iterations; Erdos_Renyi: p = %f (%d/%d), n = %d, np = %f, (1 + e) * (ln n / n) = %f"%(rep, p, m, (n*(n-1))/2, n, n * p, c))
ss = []
for bb in range(rep):
rg = igraph.Graph.Erdos_Renyi(n, p, directed = False, loops = False)
s = smallworldness_measure(g, rg)
ss.append(s)
mean_s = np.mean(ss)
return mean_s, ss
def centrality_leaders(budgetYears):
network = load_network_for(budgetYears)
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
topK = 10
candidates, rankings = cl.centrality_leaders(g)
ordered_list = []
for r in range(len(rankings))[:topK]:
#logger.info('tier: %d'%r)
for i in list(rankings[r]):
node_name = g.vs[candidates[i]]['name']
ordered_list.append(node_name)
# set the node's centrality_leader attribute, the higher the better
g.vs[candidates[i]]['centrality_leader'] = topK + 1 - r
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
filename = '%s/figures/%s-%s-centrality-leaders.png' % (
root_folder(), startBudgetYear, endBudgetYear)
draw(g, filename)
logger.info(ordered_list)
def update_graphml(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
network = load_network_for(budgetYears)
network.g.vs['centrality_leader'] = 0
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
topK = 50
candidates, rankings = cl.centrality_leaders(g)
#ordered_list = []
for r in range(len(rankings))[:topK]:
#logger.info('tier: %d'%r)
for i in list(rankings[r]):
node_name = g.vs[candidates[i]]['name']
# ordered_list.append(node_name)
# set the node's centrality_leader attribute, the higher the better
#g.vs[candidates[i]]['centrality_leader'] = topK + 1 - r
node = network.g.vs.select(name_eq=node_name)
node['centrality_leader'] = topK - r
#logger.info(topK - r)
# logger.info(node['name'])
filename = '%s/data/networks/%d-%d.graphml' % (root_folder(),
startBudgetYear, endBudgetYear)
network.write(filename)
def load_network_for(budgetYears): startBudgetYear = budgetYears[0] endBudgetYear = budgetYears[-1] filename = '%s/data/networks/%d-%d.graphml'%(root_folder(),startBudgetYear, endBudgetYear) network = ResearchCollaborationNetwork.read(filename) return network
def load_network_for(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
filename = '%s/data/networks/%d-%d.graphml' % (
root_folder(), startBudgetYear, endBudgetYear)
network = ResearchCollaborationNetwork.read(filename)
return network
def rwr_scores(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
logger.info('---------------- %s-%s -------------------' %
(startBudgetYear, endBudgetYear))
network = load_network_for(budgetYears)
#network = ResearchCollaborationNetwork.read(budgetYears)
g = network.g.copy()
ResearchCollaborationNetwork.simplify(g)
logger.info(g.summary())
adj = np.array(g.get_adjacency(igraph.GET_ADJACENCY_BOTH).data)
links = []
m = len(g.vs)
for i in range(m):
for j in range(i + 1, m):
key = '%d,%d' % (i, j)
links.append(key)
rwr_scores = pgrank.rwr_score(g, links)
rwrs = {}
for link, score in rwr_scores.items():
v = link.split(',')
v1 = int(v[0])
v2 = int(v[1])
key = '%s,%s' % (g.vs[v1]['name'], g.vs[v2]['name'])
if(float(score) > 0.001):
rwrs[key] = score
filename = '%s/data/networks/%d-%d-rwr.json' % (root_folder(),
startBudgetYear, endBudgetYear)
with open(filename, 'w') as out:
json.dump(rwrs, out)
def rwr_scores(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
logger.info('---------------- %s-%s -------------------' %
(startBudgetYear, endBudgetYear))
network = load_network_for(budgetYears)
#network = ResearchCollaborationNetwork.read(budgetYears)
g = network.g.copy()
ResearchCollaborationNetwork.simplify(g)
logger.info(g.summary())
adj = np.array(g.get_adjacency(igraph.GET_ADJACENCY_BOTH).data)
links = []
m = len(g.vs)
for i in range(m):
for j in range(i + 1, m):
key = '%d,%d' % (i, j)
links.append(key)
rwr_scores = pgrank.rwr_score(g, links)
rwrs = {}
for link, score in rwr_scores.items():
v = link.split(',')
v1 = int(v[0])
v2 = int(v[1])
key = '%s,%s' % (g.vs[v1]['name'], g.vs[v2]['name'])
if (float(score) > 0.001):
rwrs[key] = score
filename = '%s/data/networks/%d-%d-rwr.json' % (
root_folder(), startBudgetYear, endBudgetYear)
with open(filename, 'w') as out:
json.dump(rwrs, out)
def get_data(budgetYears): network = load_network_for(budgetYears) wg = network.g.copy() wg = ResearchCollaborationNetwork.simplify(wg) degree = np.array(wg.degree(), dtype=np.int) strength = np.array(wg.strength(loops=False,weights=wg.es['weight']), dtype=np.int) return wg, degree, strength
def average_strength_for(budgetYears):
logger.info(budgetYears)
network = load_network_for(budgetYears)
g = network.g.copy()
# pick the largest component of the network, the subgraph without any isolated nodes (nodes that are not connected to any other nodes)
g = ResearchCollaborationNetwork.largest_component(g)
g = set_category_by_is_ctsa(g, refG)
logger.info('ctsa: %0.2f'%average_strength(g, 1.0))
logger.info('non-ctsa: %0.2f'%average_strength(g, 0.0))
def draw_g(budgetYears): network = load_network_for(budgetYears) g = network.g.copy() #g = g.simplify(multiple=True, loops=True,combine_edges=sum) # convert to undirected #g.to_undirected(combine_edges=sum) g = ResearchCollaborationNetwork.simplify(g) startBudgetYear = budgetYears[0] endBudgetYear = budgetYears[-1] filename = '%s/figures/%s-%s-%d.png'%(root_folder(),startBudgetYear, endBudgetYear,len(g.vs)) #logger.info(g.summary()) draw(g, filename) gl = ResearchCollaborationNetwork.largest_component(g) filename = '%s/figures/%s-%s-%d-largest-component.png'%(root_folder(),startBudgetYear, endBudgetYear,len(gl.vs)) draw(gl, filename)
def average_shortest_path_for(budgetYears):
logger.info(budgetYears)
network = load_network_for(budgetYears)
g = network.g.copy()
# pick the largest component of the network, the subgraph without any isolated nodes (nodes that are not connected to any other nodes)
g = ResearchCollaborationNetwork.largest_component(g)
g = set_category_by_is_ctsa(g, refG)
weights = [ 1/weight for weight in g.es['weight']]
logger.info('within non-CTSA investigators: %0.3f'%average_shortest_path(g, weights = weights, source = 0.0, target = 0.0))
logger.info('within CTSA investigators: %0.3f'%average_shortest_path(g, weights = weights, source=1.0, target = 1.0))
#logger.info('from CTSA to non-CTSA: %0.3f'%average_shortest_path(g, weights = weights, source = 1.0, target = 0.0))
logger.info('from non-CTSA to all: %0.3f'%average_shortest_path(g, weights = weights, source = 0.0, target = None))
logger.info('from CTSA to all: %0.3f'%average_shortest_path(g, weights = weights, source = 1.0, target = None))
def network_to_d3(budgetYears):
network = load_network_for(budgetYears)
#network = ResearchCollaborationNetwork.read(budgetYears)
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
filename = '%s/data/networks/%s-%s-complete.json' % (
root_folder(), startBudgetYear, endBudgetYear)
ResearchCollaborationNetwork.d3(network.g, filename)
# remove isolated nodes
g = network.g.copy()
g = ResearchCollaborationNetwork.simplify(g)
filename = '%s/data/networks/%s-%s.json' % (root_folder(), startBudgetYear,
endBudgetYear)
ResearchCollaborationNetwork.d3(g, filename)
# only the largest components
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
filename = '%s/data/networks/%s-%s-largest-component.json' % (
root_folder(), startBudgetYear, endBudgetYear)
ResearchCollaborationNetwork.d3(g, filename)
def network_to_d3(budgetYears):
network = load_network_for(budgetYears)
#network = ResearchCollaborationNetwork.read(budgetYears)
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
filename = '%s/data/networks/%s-%s-complete.json' % (root_folder(),
startBudgetYear, endBudgetYear)
ResearchCollaborationNetwork.d3(network.g, filename)
# remove isolated nodes
g = network.g.copy()
g = ResearchCollaborationNetwork.simplify(g)
filename = '%s/data/networks/%s-%s.json' % (root_folder(),
startBudgetYear, endBudgetYear)
ResearchCollaborationNetwork.d3(g, filename)
# only the largest components
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
filename = '%s/data/networks/%s-%s-largest-component.json' % (root_folder(),
startBudgetYear, endBudgetYear)
ResearchCollaborationNetwork.d3(g, filename)
def update_graphml(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
network = load_network_for(budgetYears)
network.g.vs['centrality_leader'] = 0
g = network.g.copy()
g = ResearchCollaborationNetwork.largest_component(g)
topK = 50
candidates, rankings = cl.centrality_leaders(g)
#logger.info(candidates)
#logger.info(rankings)
#ordered_list = []
for r in range(len(rankings))[:topK]:
logger.info('tier: %d' % r)
for i in list(rankings[r]):
node_name = g.vs[candidates[i]]['name']
# ordered_list.append(node_name)
# set the node's centrality_leader attribute, the higher the better
#g.vs[candidates[i]]['centrality_leader'] = topK + 1 - r
node = network.g.vs.select(name_eq=node_name)
#logger.info(node['name'])
node['centrality_leader'] = r + 1
#logger.info(topK - r)
# logger.info(node['name'])
filename = '%s/data/networks/%d-%d.graphml' % (
root_folder(), startBudgetYear, endBudgetYear)
network.write(filename)
def per_network(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
logger.info('---------------- %s-%s -------------------'%(startBudgetYear, endBudgetYear))
network = load_network_for(budgetYears)
g = network.g.copy()
ResearchCollaborationNetwork.simplify(g)
logger.info(g.summary())
# randomly pick 20 users
candidates = range(len(g.vs))
shuffle(candidates)
candidates = candidates[:20]
adj = np.array(g.get_adjacency(igraph.GET_ADJACENCY_BOTH).data)
m, _ = adj.shape
nonobservedlinks = {}
nonobserved_actual_edges = []
nonobserved_nonexist_edges = []
for i in range(m):
# undirectd graph, so only care if the source is in candidates or not
if i not in candidates:
continue
for j in range(i + 1, m):
key = '%d,%d'%(i,j)
nonobservedlinks[key] = adj[i,j]
if adj[i,j] > 0:
nonobserved_actual_edges.append(key)
else:
nonobserved_nonexist_edges.append(key)
#logger.info('-----original graph:-----\r\n %s \r\n -----end original graph:-----'%g.summary())
auc = 0.0
apk = {3: 0.0, 5: 0.0, 10: 0.0}
kfold = 10
cnt = 0;
roc_samples = []
for ((es_p_training, es_p_validation), (es_m_training, es_m_validation)) in zip(utils.k_fold_cross_validation(list(nonobserved_actual_edges), kfold), utils.k_fold_cross_validation(list(nonobserved_nonexist_edges), kfold)):
logger.info('--------iteration %d-------------'%cnt)
logger.info('xxxxxxxxxxxxxxxxxxxxxxxx')
logger.info('positive training: %d'%len(es_p_training))
logger.info('positive validation: %d'%len(es_p_validation))
logger.info('------------------------')
logger.info('negative training: %d'%len(es_m_training))
logger.info('negative validation: %d'%len(es_m_validation))
#logger.info('xxxxxxxxxxxxxxxxxxxxxxxx')
training = es_p_training + es_m_training
validation = es_p_validation + es_m_validation
#logger.info('training: %d; valiation: %d'%(len(training), len(validation)))
# create training graph
trainingG = g.copy()
edges_2_delete = []
#// remove edges from the validation set
for link in validation:
v = link.split(',')
v1 = int(v[0])
v2 = int(v[1])
eId = trainingG.get_eid(v1,v2, directed=False, error=False)
if eId != -1:
edges_2_delete.append(eId)
trainingG.delete_edges(edges_2_delete)
#logger.info('-----training graph:-----\r\n %s \r\n -----end training graph:-----'%trainingG.summary())
rwr_scores = pgrank.rwr_score(trainingG, validation)
actual = []
posterior = []
actual_edges = []
for k in validation:
actual.append(nonobservedlinks[k])
if nonobservedlinks[k] > 0:
actual_edges.append(k)
posterior.append(rwr_scores[k])
roc_samples.append((k, nonobservedlinks[k], rwr_scores[k]))
#logger.info('actual edges: %s'%actual_edges)
#logger.info('posterior: %s'%posterior)
auc_ = benchmarks.auc(actual, posterior)
auc += auc_
#area, [ax, lines] = roc.roc_curve(labels=np.array(actual),scores=np.array(posterior))
for topK, p in apk.iteritems():
predictedIndexes = sorted(range(len(posterior)), reverse=True, key=lambda k: posterior[k])[:topK]
predicted = np.array(validation)[predictedIndexes]
apk_ = benchmarks.apk(actual_edges, predicted, topK)
apk[topK] += apk_
cnt += 1
# take a look at http://www.machinedlearnings.com/2012/06/thought-on-link-prediction.html
logger.info('auc: %f'%(auc/kfold))
for topK, p in apk.iteritems():
logger.info('ap@%d: %f'%(topK, (apk[topK]/kfold)))
#plt.show()
np.save('%s/data/%s-%s.per_network.roc.samples.npy'%(root_folder(),startBudgetYear, endBudgetYear), np.array(roc_samples))
def network_characteristics(budgetYears):
logger.info(
"================================================================")
logger.info(budgetYears)
network = load_network_for(budgetYears)
g = network.g.copy()
# simplified network is the one without any isolated nodes (nodes that are not connected to any other nodes)
g = ResearchCollaborationNetwork.simplify(g)
logger.info('# of nodes: %d' % (len(g.vs)))
logger.info('# of edges: %d' % (len(g.es)))
logger.info('density: %.3f' % (g.density()))
new_edges = 0.0
# 2006 is the baseline
if budgetYears[0] > 2006:
if budgetYears[0] == 2010 and budgetYears[-1] == 2012:
pBudgetYears = range(2006, 2010)
else:
pBudgetYears = np.array(budgetYears) - 1
pNetwork = load_network_for(pBudgetYears)
pg = pNetwork.g.copy()
pg = ResearchCollaborationNetwork.simplify(pg)
new_edges = average_number_of_new_edges(g, pg)
logger.info('average number of new edges: %.3f' % new_edges)
logger.info('# of isolated components: %d' %
(num_of_isolated_components(g)))
# only the largest component, mainly because shortest path length is rather arbitrary on graphs with isolated components, which our RCNs are.
g = ResearchCollaborationNetwork.largest_component(g)
weights = g.es['weight']
r_weights = [1 / float(weight) for weight in g.es['weight']]
no_weigths = [1 for weight in g.es['weight']]
logger.info('# of nodes (largest component): %d' % (len(g.vs)))
logger.info('# of edges (largest component): %d' % (len(g.es)))
C_g = g.transitivity_avglocal_undirected(mode='zero', weights=no_weigths)
logger.info('C_g (weights = None): %.3f' % C_g)
C_wg = g.transitivity_avglocal_undirected(mode='zero', weights=weights)
logger.info('C_g (weights = number of collaborations): %.3f' % C_wg)
C_tg = g.transitivity_undirected(mode='zero')
logger.info('C_g (triplets definition): %.3f' % C_tg)
L_g = average_shortest_path_length_weighted(g, no_weigths)
logger.info("L_g (weights = 1): %.3f" % L_g)
L_wg = average_shortest_path_length_weighted(g, r_weights)
logger.info("L_g (weights = 1/weights): %.3f" % L_wg)
D_wg = diversity(g, r_weights)
logger.info("D_g (weights = 1/weights): %.3f" % D_wg)
def per_candidate(budgetYears):
startBudgetYear = budgetYears[0]
endBudgetYear = budgetYears[-1]
logger.info('---------------- %s-%s -------------------'%(startBudgetYear, endBudgetYear))
network = load_network_for(budgetYears)
g = network.g.copy()
ResearchCollaborationNetwork.simplify(g)
logger.info(g.summary())
adj = np.array(g.get_adjacency(igraph.GET_ADJACENCY_BOTH).data)
m, _ = adj.shape
cNodes = g.vs.select(_degree_gt=15) #range(len(g.vs))
candidates = []
for cNode in cNodes:
candidates.append(cNode.index)
shuffle(candidates)
candidates = candidates[:10]
total_auc = 0.0
precision_at_k = {3: 0.0, 5: 0.0, 10: 0.0}
mapk = precision_at_k
kfold = 5
roc_samples = []
progress = len(candidates)
# for each candidate we do training and testing...
for c in candidates:
logger.info('%d-----------------------'%progress)
nonobservedlinks = {}
nonobserved_actual_edges = []
nonobserved_nonexist_edges = []
# undirectd graph, so only care if the source is in candidates or not
for j in range(m):
key = '%d,%d'%(c,j)
nonobservedlinks[key] = adj[c,j]
#logger.info(adj[c,j])
if adj[c,j] > 0:
nonobserved_actual_edges.append(key)
else:
nonobserved_nonexist_edges.append(key)
cnt = 0
auc = 0.0
#average precision at k is defined per candidate
apk = precision_at_k
for ((es_p_training, es_p_validation), (es_m_training, es_m_validation)) in zip(utils.k_fold_cross_validation(list(nonobserved_actual_edges), kfold), utils.k_fold_cross_validation(list(nonobserved_nonexist_edges), kfold)):
#logger.info('--------iteration %d-------------'%cnt)
#logger.info('xxxxxxxxxxxxxxxxxxxxxxxx')
#logger.info('positive training: %d'%len(es_p_training))
#logger.info('positive validation: %d'%len(es_p_validation))
#logger.info('------------------------')
#logger.info('negative training: %d'%len(es_m_training))
#logger.info('negative validation: %d'%len(es_m_validation))
#logger.info('xxxxxxxxxxxxxxxxxxxxxxxx')
training = es_p_training + es_m_training
validation = es_p_validation + es_m_validation
#logger.info('training: %d; valiation: %d'%(len(training), len(validation)))
# create training graph
trainingG = g.copy()
edges_2_delete = []
#// remove edges from the validation set
for link in validation:
v = link.split(',')
v1 = int(v[0])
v2 = int(v[1])
eId = trainingG.get_eid(v1,v2, directed=False, error=False)
if eId != -1:
edges_2_delete.append(eId)
trainingG.delete_edges(edges_2_delete)
#logger.info('-----training graph:-----\r\n %s \r\n -----end training graph:-----'%trainingG.summary())
rwr_scores = pgrank.rwr_score(trainingG, validation)
for k, rwr_score in rwr_scores.iteritems():
if rwr_score > 1:
logger.info('overflow? rwr_score: %0.2f'%(rwr_score))
actual = []
posterior = []
actual_edges = []
for k in validation:
actual.append(nonobservedlinks[k])
if nonobservedlinks[k] > 0:
actual_edges.append(k)
posterior.append(rwr_scores[k])
roc_samples.append((k, nonobservedlinks[k], rwr_scores[k]))
#logger.info('actual edges: %s'%actual_edges)
#logger.info('posterior: %s'%posterior)
auc_ = benchmarks.auc(actual, posterior)
auc += auc_
total_auc += auc_
#area, [ax, lines] = roc.roc_curve(labels=np.array(actual),scores=np.array(posterior))
for topK, p in mapk.iteritems():
predictedIndexes = sorted(range(len(posterior)), reverse=True, key=lambda k: posterior[k])[:topK]
predicted = np.array(validation)[predictedIndexes]
apk_ = benchmarks.apk(actual_edges, predicted, topK)
apk[topK] += apk_
mapk[topK] += apk_
cnt += 1
logger.info('%d: auc: %f'%(c, float(auc)/kfold))
for topK, p in apk.iteritems():
logger.info('%d: ap@%d: %f'%(c, topK, (apk[topK]/kfold)))
progress -= 1
logger.info('auc: %f'%(float(total_auc)/(kfold*len(candidates))))
for topK, p in mapk.iteritems():
logger.info('map@%d: %f'%(topK, (mapk[topK]/(kfold*len(candidates)))))
np.save('%s/data/%s-%s.per_user.roc.samples.npy'%(root_folder(),startBudgetYear, endBudgetYear), np.array(roc_samples))
def network_characteristics(budgetYears):
logger.info("================================================================")
logger.info(budgetYears)
network = load_network_for(budgetYears)
g = network.g.copy()
# simplified network is the one without any isolated nodes (nodes that are not connected to any other nodes)
g = ResearchCollaborationNetwork.simplify(g)
logger.info('# of nodes: %d'%(len(g.vs)))
logger.info('# of edges: %d'%(len(g.es)))
logger.info('density: %.3f'%(g.density()))
new_edges = 0.0
# 2006 is the baseline
if budgetYears[0] > 2006:
if budgetYears[0] == 2010 and budgetYears[-1] == 2012:
pBudgetYears = range(2006,2010)
else:
pBudgetYears = np.array(budgetYears) - 1
pNetwork = load_network_for(pBudgetYears)
pg = pNetwork.g.copy()
pg = ResearchCollaborationNetwork.simplify(pg)
new_edges = average_number_of_new_edges(g, pg)
logger.info('average number of new edges: %.3f'%new_edges)
logger.info('# of isolated components: %d'%(num_of_isolated_components(g)))
# only the largest component, mainly because shortest path length is rather arbitrary on graphs with isolated components, which our RCNs are.
g = ResearchCollaborationNetwork.largest_component(g)
weights = g.es['weight']
r_weights = [ 1/float(weight) for weight in g.es['weight']]
no_weigths = [ 1 for weight in g.es['weight']]
logger.info('# of nodes (largest component): %d'%(len(g.vs)))
logger.info('# of edges (largest component): %d'%(len(g.es)))
C_g = g.transitivity_avglocal_undirected(mode='zero', weights=no_weigths)
logger.info('C_g (weights = None): %.3f'%C_g)
C_wg = g.transitivity_avglocal_undirected(mode='zero', weights=weights)
logger.info('C_g (weights = number of collaborations): %.3f'%C_wg)
C_tg = g.transitivity_undirected(mode='zero')
logger.info('C_g (triplets definition): %.3f'%C_tg)
L_g = average_shortest_path_length_weighted(g, no_weigths)
logger.info("L_g (weights = 1): %.3f"%L_g)
L_wg = average_shortest_path_length_weighted(g, r_weights)
logger.info("L_g (weights = 1/weights): %.3f"%L_wg)
D_wg = diversity(g, r_weights)
logger.info("D_g (weights = 1/weights): %.3f"%D_wg)