def significance(self):
"""
Significance estimates how likely a partition of dense communities appear in a random graph.
:return: the significance score
:Example:
>>> from cdlib.algorithms import louvain
>>> g = nx.karate_club_graph()
>>> communities = louvain(g)
>>> mod = communities.significance()
:References:
Traag, V. A., Aldecoa, R., & Delvenne, J. C. (2015). **Detecting communities using asymptotical surprise.** Physical Review E, 92(2), 022816.
"""
if self.__check_graph():
return evaluation.significance(self.graph, self)
else:
raise ValueError("Graph instance not specified")
def test_significance(self):
g = nx.karate_club_graph()
communities = louvain(g)
mod = evaluation.significance(g, communities)
self.assertGreaterEqual(mod.score, 0)
def getAllScoresDict(g, _reference, _communities, executionTime):
scores = {}
scores['time'] = executionTime
reference = copy.deepcopy(_reference)
reference.communities = complete_partition(reference.communities, g, mode='new_cluster')
communities = copy.deepcopy(_communities)
communities.communities = complete_partition(communities.communities, g, mode='new_cluster')
# scores['adjusted_mutual_information'] = evaluation.adjusted_mutual_information(reference,communities).score
# returns MatchingResult object
# scores['adjusted_rand_index'] = evaluation.adjusted_rand_index(reference,communities).score
# Compute the average F1 score of the optimal algorithms matches among the partitions in input.
try:
scores['f1'] = evaluation.f1(reference, communities).score
except:
scores['f1'] = np.nan
# Compute the Normalized F1 score of the optimal algorithms matches among the partitions in input.
try:
scores['nf1'] = evaluation.nf1(reference, communities).score
except:
scores['nf1'] = np.nan
# Normalized Mutual Information between two clusterings.
# scores['normalized_mutual_information'] = evaluation.normalized_mutual_information(reference, communities)[0]
# Index of resemblance for overlapping, complete coverage, network clusterings.
try:
scores['omega'] = evaluation.omega(reference, communities).score
except:
scores['omega'] = np.nan
# Overlapping Normalized Mutual Information between two clusterings.
try:
scores['overlapping_normalized_mutual_information_LFK'] = evaluation.overlapping_normalized_mutual_information_LFK(reference, communities)[0]
except:
scores['overlapping_normalized_mutual_information_LFK'] = np.nan
# Overlapping Normalized Mutual Information between two clusterings.
# scores['overlapping_normalized_mutual_information_MGH'] = evaluation.overlapping_normalized_mutual_information_MGH(reference, communities)[0]
# Variation of Information among two nodes partitions.
# scores['variation_of_information'] = evaluation.variation_of_information(reference, communities)[0]
# scores['avg_distance'] = evaluation.avg_distance(g,communities, summary=True)
try:
scores['avg_embeddedness'] = evaluation.avg_embeddedness(g,communities, summary=True).score
except:
scores['avg_embeddedness'] = np.nan
try:
scores['average_internal_degree'] = evaluation.average_internal_degree(g,communities, summary=True).score
except:
scores['average_internal_degree'] = np.nan
# scores['avg_transitivity'] = evaluation.avg_transitivity(g,communities, summary=True)
# Fraction of total edge volume that points outside the community.
try:
scores['conductance'] = evaluation.conductance(g,communities, summary=True).score
except:
scores['conductance'] = np.nan
# Fraction of existing edges (out of all possible edges) leaving the community.
try:
scores['cut_ratio'] = evaluation.cut_ratio(g,communities, summary=True).score
except:
scores['cut_ratio'] = np.nan
# Number of edges internal to the community
try:
scores['edges_inside'] = evaluation.edges_inside(g,communities, summary=True).score
except:
scores['edges_inside'] = np.nan
# Number of edges per community node that point outside the cluster
try:
scores['expansion'] = evaluation.expansion(g,communities, summary=True).score
except:
scores['expansion'] = np.nan
# Fraction of community nodes of having internal degree higher than the median degree value.
try:
scores['fraction_over_median_degree'] = evaluation.fraction_over_median_degree(g,communities, summary=True).score
except:
scores['fraction_over_median_degree'] = np.nan
# The hub dominance of a community is defined as the ratio of the degree of its most connected node w.r.t. the theoretically maximal degree within the community.
# scores['hub_dominance'] = evaluation.hub_dominance(g,communities, summary=True)
# The internal density of the community set.
try:
scores['internal_edge_density'] = evaluation.internal_edge_density(g,communities, summary=True).score
except:
scores['internal_edge_density'] = np.nan
# Normalized variant of the Cut-Ratio
try:
scores['normalized_cut'] = evaluation.normalized_cut(g,communities, summary=True).score
except:
scores['normalized_cut'] = np.nan
# Maximum fraction of edges of a node of a community that point outside the community itself.
# scores['max_odf'] = evaluation.max_odf(g,communities, summary=True)
# Average fraction of edges of a node of a community that point outside the community itself.
# scores['avg_odf'] = evaluation.avg_odf(g,communities, summary=True)
# Fraction of nodes in S that have fewer edges pointing inside than to the outside of the community.
# scores['flake_odf'] = evaluation.flake_odf(g,communities, summary=True)
# The scaled density of a community is defined as the ratio of the community density w.r.t. the complete graph density.
try:
scores['scaled_density'] = evaluation.scaled_density(g,communities, summary=True).score
except:
scores['scaled_density'] = np.nan
# Significance estimates how likely a partition of dense communities appear in a random graph.
try:
scores['significance'] = evaluation.significance(g,communities).score
except:
scores['significance'] = np.nan
# Size is the number of nodes in the community
try:
scores['size'] = evaluation.size(g,communities, summary=True).score
except:
scores['size'] = np.nan
# Surprise is statistical approach proposes a quality metric assuming that edges between vertices emerge randomly according to a hyper-geometric distribution.
# According to the Surprise metric, the higher the score of a partition, the less likely it is resulted from a random realization, the better the quality of the community structure.
try:
scores['surprise'] = evaluation.surprise(g,communities).score
except:
scores['surprise'] = np.nan
try:
scores['modularity_density'] = evaluation.modularity_density(g,communities).score
except:
scores['modularity_density'] = np.nan
# Fraction of community nodes that belong to a triad.
# scores['triangle_participation_ratio'] = evaluation.triangle_participation_ratio(g,communities, summary=True)
# Purity is the product of the frequencies of the most frequent labels carried by the nodes within the communities
# scores['purity'] = evaluation.purity(communities)
return scores
forDf['method'].append(method)
forDf['score'].append(score)
df = pd.DataFrame(forDf)
df.to_csv('cdlib_results_legacy_part.csv')
graphStatistics = {'graph': [], 'statistic': [], 'value':[]}
statistics = {
'$|V|$': lambda graph, reference: len(graph.nodes),
'$|E|$': lambda graph, reference: len(graph.edges),
'$\\hat{k}$': lambda graph, reference: len(reference.communities),
'$\\hat{o}$': lambda graph, reference: getOverlappingNumber(reference.communities),
'$\\hat{c}$': lambda graph, reference: nx.average_clustering(graph),
'\\shortstack[l]{normalized \\\\ cut}': lambda graph, reference: evaluation.normalized_cut(graph,reference, summary=True).score,
'\\shortstack[l]{internal \\\\ edge \\\\density}': lambda graph, reference: evaluation.internal_edge_density(graph,reference, summary=True).score,
'significance': lambda graph, reference: evaluation.significance(graph,reference, summary=True).score,
'\\shortstack[l]{avarage \\\\ internal \\\\degree}': lambda graph, reference: evaluation.average_internal_degree(graph,reference, summary=True).score,
'\\shortstack[l]{modularity \\\\ density}': lambda graph, reference: evaluation.modularity_density(graph,reference).score,
}
for graph, name, reference in zip(graphs, names, references):
for statistic_name, statistic in statistics.items():
graphStatistics['graph'].append(name)
graphStatistics['statistic'].append(statistic_name)
graphStatistics['value'].append(statistic(graph, reference) )
graphStatisticsDF = pd.DataFrame(graphStatistics)
graphStatisticsDF.to_csv('../Results/graphs_stats_legacy.csv')
# method that were not used, or don't work by some reason
