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 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 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 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 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 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 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 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 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 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 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)
