def network_structure_calculations(sn):
g = sn.g
_transitivity = transitivity(g)
_average_clustering = average_clustering(g)
size_biggest_component = -1
connected_components = 0
ave_short_path_biggest = -1
for sg in nx.connected_component_subgraphs(g, False):
connected_components += 1
if len(sg) > size_biggest_component:
size_biggest_component = len(sg)
ave_short_path_biggest = average_shortest_path_length(sg)
return (_transitivity,_average_clustering,
connected_components, size_biggest_component,
ave_short_path_biggest)
def runWith(fname) :
print(fname)
gm=dr.GraphMaker()
gm.load(fname)
# dpr=gm.pagerank()
dg=gm.graph()
#for x in dg: print('VERT::', x)
print('nodes:', dg.number_of_nodes())
print('edges:', dg.number_of_edges())
comps=nx.strongly_connected_components(dg)
print('strongly connected components:',len(list(comps)))
c = max(nx.strongly_connected_components(dg), key=len)
mg=dg.subgraph(c)
print('attracting components:', co.number_attracting_components(dg))
print('number_weakly_connected_components:',co.number_weakly_connected_components(dg))
print('Transitivity:',cl.transitivity(dg))
return
e=dm.eccentricity(mg)
dprint('ecc:', e)
cent=dm.center(mg,e=e)
print('CENTER',cent)
p=dm.periphery(mg,e=e)
print('perif:', len(list(e)))
#dprint('perif:', e)
print('diameter:', dm.diameter(nx.Graph(mg)))
print('radius:', dm.radius(nx.Graph(mg)))
g = nx.Graph(dg)
print('omega:', omega(g))
print('sigma:', sigma(g))
def random_attack2(graph, nodes_number, iteration_removals):
# lista onde estão os valores de clusterização da rede depois da remoção dos nos
after_removals = []
lenght_range = int((nodes_number - iteration_removals)/iteration_removals)
# retorna um set, com os nos que representam o maior componente conexo da rede
# print('largest cc: {}'.format(largest_cc))
for _ in tqdm(range(lenght_range)):
# se o tamanho do maior componente conexo por menor que o número de nos que quero remover, sair do loop
largest_cc = max(networkx.connected_components(graph), key=len)
print(len(largest_cc))
if len(largest_cc) < iteration_removals:
break
removals_set = set(random.sample(largest_cc, iteration_removals))
# print('remocoes: {}'.format(removals_set))
largest_cc = largest_cc - removals_set
# remove iterations_removals do maior componente conexo da rede
graph.remove_nodes_from(removals_set)
after_removals.append(nx_cluster.transitivity(graph))
# after_removals.append(np.mean(list(nx_cluster.transitivity(graph).values())))
return after_removals
def ii_two_core_test(C, ii_key):
if core.core_number(C)[ii_key] == 2:
return (1)
else:
return (0)
ii_two_core_test = ii_two_core_test(C, ii_key)
#print(ii_two_core_test)
# [9] Transitivity
# Def : the proportion of all triads that exhibit closure in the network
# Outputs a float representing 3 (triangles / triads).
transitivity = transitivity.transitivity(C)
# [10] Diameter
# Def : The diameter is the maximum eccentricity.
# The eccentricity of a node v is the maximum distance from v to all other nodes in G.
diameter = diameter.diameter(C)
# ______________________________________________________________________________
# How to display the network. pylab.show() is necessary if not in the interactive
# mode. Enter into interactive mode by typing ipython -pylab in the cmd.
options = {
'node_color': 'grey',
def getGlobalClusteringCoefficient(self) -> float:
"""
"""
return transitivity(self.graph)
return gt_stats.vertex_hist(g, 'total')[1][-2]
def page_rank(g):
# return gt_stats.vertex_hist(g, gt.pagerank(g))
return gt.pagerank(g).get_array()
def variance(g):
degree_hist = gt_stats.vertex_hist(g, 'total')[0] / g.num_vertices()
second_m = np.sum(degree_hist * (np.arange(len(degree_hist)) ** 2))
return second_m - avg_degree(g) ** 2
if __name__ == '__main__':
nx_g = barabasi_albert_graph(int(1e3), 2)
nx_apl = average_shortest_path_length(nx_g)
nx_ad = 2 * nx_g.number_of_edges() / nx_g.number_of_nodes()
nx_gcc = transitivity(nx_g)
nx_lcc = average_clustering(nx_g)
nx_md = len(degree_histogram(nx_g)) - 1
nx_drogc = max(connected_component_subgraphs(nx_g), key=len).number_of_nodes() / nx_g.number_of_nodes()
second_m = np.sum(np.array(degree_histogram(nx_g)) * (np.arange(len(degree_histogram(nx_g))) ** 2))
nx_v = math.sqrt(second_m - nx_ad ** 2)
nx_ap = degree_pearson_correlation_coefficient(nx_g)
nx_aknn = np.flip(np.array(
[it[1] for it in sorted(
average_degree_connectivity(nx_g).items(), reverse=True
)]
))
nx_dh = np.array(degree_histogram(nx_g)) / nx_g.number_of_nodes()
nx_cdh = np.flip(np.flip(
(np.array(degree_histogram(nx_g)) / nx_g.number_of_nodes())
def compute_directed_graph_metrics(G):
assert type(G) is nx.DiGraph
n_edges = len(G.edges)
# in & out degree stats
in_degrees = np.array([n for _, n in G.in_degree()])
out_degrees = np.array([n for _, n in G.out_degree()])
in_degrees_k_freq = np.unique(in_degrees, return_counts=True)[1]
out_degrees_k_freq = np.unique(out_degrees, return_counts=True)[1]
out_in_degrees_corr = numeric_attribute_correlation(
G, dict(G.out_degree), dict(G.in_degree))
# dyad metrics
dyad_freq = dyadic_census(G)
dyad_metrics = compute_dyad_metrics(dyad_freq)
# reciprocity
reciprocity = None
if n_edges > 0:
# based on networkx definition
reciprocity = 2 * dyad_freq["2"] / (dyad_freq["1"] +
2 * dyad_freq["2"])
# clustering
global_clustering = transitivity(G)
local_clustering_mean = average_clustering(G)
# fraction of connected node pairs (any path len)
f_connected_node_pairs = fraction_of_connected_node_pairs(G)
# centralization
cent_metrics = centralization_metrics(G, prefix="_di")
metrics = {
"n_edges_di":
len(G.edges),
"density_di":
density(G),
"reciprocity":
reciprocity,
# in_degree
"in_degrees_mean":
safe(np.mean, in_degrees),
"in_degrees_var":
safe(np.var, in_degrees),
"in_degrees_hidx":
safe(h_index, in_degrees),
"in_degrees_gini":
safe(gini, in_degrees + eps),
"in_degrees_f0":
safe(np.mean, (in_degrees == 0)),
"in_degrees_pk_ent":
entropy(in_degrees_k_freq),
"in_degrees_pk_gini":
gini(in_degrees_k_freq),
# out_degree
"out_degrees_mean":
safe(np.mean, out_degrees),
"out_degrees_var":
safe(np.var, out_degrees),
"out_degrees_hidx":
safe(h_index, out_degrees),
"out_degrees_gini":
safe(gini, out_degrees + eps),
"out_degrees_f0":
safe(np.mean, (out_degrees == 0)),
"out_degrees_pk_ent":
entropy(out_degrees_k_freq),
"out_degrees_pk_gini":
gini(out_degrees_k_freq),
# degree assortativity
"out_in_degrees_corr":
out_in_degrees_corr,
# dyad metric
**dyad_metrics,
# fraction of connected node pairs with path of any length
"f_connected_node_pairs_di":
f_connected_node_pairs,
# clustering coefficients
"global_clustering_di":
global_clustering,
"local_clustering_mean_di":
local_clustering_mean,
# centralization
**cent_metrics
}
return metrics
def compute_undirected_graph_metrics(G):
assert type(G) is nx.Graph
# degrees stats
degrees = np.array([i for _, i in G.degree])
degrees_k_freq = np.unique(degrees, return_counts=True)[1]
degrees_corr = numeric_attribute_correlation(G, dict(G.degree),
dict(G.degree))
# clustering
global_clustering = transitivity(G)
local_clustering_mean = average_clustering(G)
# fraction of connected node pairs (any path len)
f_connected_node_pairs = fraction_of_connected_node_pairs(G)
# centralization
cent_metrics = centralization_metrics(G, prefix="_ud")
# modularity
modularity_metrics = compute_modularity_metrics(G)
# largest CC
CC1_nodes = max(connected_components(G), key=len)
CC1 = G.subgraph(CC1_nodes).copy()
f_CC1_nodes = len(CC1) / len(G)
# algebraic_connectivity of the largest CC
algebraic_connectivity_CC1 = None
if len(CC1) > 2:
try:
algebraic_connectivity_CC1 = algebraic_connectivity(CC1, seed=0)
except:
algebraic_connectivity_CC1 = None
# connected components
CC = connected_components(G)
CC_sizes = np.array([len(cc_i) for cc_i in CC])
CC_metrics = {}
for k in CC_k_thresholds:
CC_metrics[f"n_CC_{k}"] = np.sum(CC_sizes >= k)
# k-core
k_core_metrics = {}
G_core_number = core_number(G)
for k in k_core_ks:
k_core_subgraph = k_core(G, k=k, core_number=G_core_number)
k_core_metrics[f"core_{k}_n_nodes"] = len(k_core_subgraph.nodes)
k_core_metrics[f"core_{k}_n_edges"] = len(k_core_subgraph.edges)
k_core_metrics[f"core_{k}_density"] = density(k_core_subgraph)
k_core_metrics[f"core_{k}_n_CC"] = len(
list(connected_components(k_core_subgraph)))
# k-truss
k_truss_metrics = {}
for k in k_truss_ks:
k_truss_subgraph = k_truss(G, k=k)
k_truss_metrics[f"truss_{k}_n_nodes"] = len(k_truss_subgraph.nodes)
k_truss_metrics[f"truss_{k}_n_edges"] = len(k_truss_subgraph.edges)
k_truss_metrics[f"truss_{k}_density"] = density(k_truss_subgraph)
k_truss_metrics[f"truss_{k}_n_CC"] = len(
list(connected_components(k_truss_subgraph)))
metrics = {
"n_edges_ud":
len(G.edges()),
"density_ud":
density(G),
# degree stats
"degrees_mean":
safe(np.mean, degrees),
"degrees_var":
safe(np.var, degrees),
"degrees_hidx":
safe(h_index, degrees),
"degrees_gini":
safe(gini, degrees + eps),
"degrees_f0":
safe(np.mean, (degrees == 0)),
"degrees_corr":
degrees_corr,
"degrees_pk_ent":
entropy(degrees_k_freq),
"degrees_pk_gini":
gini(degrees_k_freq),
# fraction of connected node pairs with path of any length
"f_connected_node_pairs_ud":
f_connected_node_pairs,
# clustering coefficients
"global_clustering_ud":
global_clustering,
"local_clustering_mean_ud":
local_clustering_mean,
# centralization
**cent_metrics,
# modularity
**modularity_metrics,
# fraction of nodes in the largest CC
"f_CC1_nodes":
f_CC1_nodes,
# algebraic connectivity of the largest CC
"algebraic_connectivity_CC1":
algebraic_connectivity_CC1,
# connected components
**CC_metrics,
# k-core
**k_core_metrics,
# k-truss
**k_truss_metrics
}
return metrics
graph_nx = networkx.waxman_graph(20) graph_ig = igraph.Graph(len(graph_nx), list(zip(*list(zip(*networkx.to_edgelist(graph_nx)))[:2]))) import numpy as np import networkx.algorithms.cluster as nx_cluster cluster_nx = np.mean(list(nx_cluster.clustering(graph_nx).values())) cluster_nx nx_cluster.clustering(graph_nx).values() graph_nx = networkx.waxman_graph(100) nx_cluster.clustering(graph_nx).values() cluster_nx = np.mean(list(nx_cluster.clustering(graph_nx).values())) cluster_nx graph_ig = igraph.Graph(len(graph_nx), list(zip(*list(zip(*networkx.to_edgelist(graph_nx)))[:2]))) graph_ig.transitivity_avglocal_undirected() graph_ig.transitivity_undirected() graph_ig.transitivity_local_undirected() cluster_ig = np.mean(graph_ig.transitivity_local_undirected()) cluster_ig np.mean(graph_ig.transitivity_local_undirected()) graph_ig.transitivity_local_undirected() cluster_ig = graph_ig.transitivity_local_undirected() cluster_ig np.nan_to_num(cluster_ig) cluster_ig cluster_ig = np.nan_to_num(cluster_ig) cluster_ig np.mean(cluster_ig) nx_cluster.transitivity(graph_nx) graph_ig.transitivity_avglocal_undirected() graph_ig.transitivity_undirected()
