Evaluation

The evaluation of Community Discovery algorithms is not an easy task. CDlib implements two families of evaluation strategies:

  • Internal evaluation through quality scores
  • External evaluation through partitions comparison

Fitness Functions

Fitness functions allows to summarize the characteristics of a computed set of communities. CDlib implements the following quality scores:

average_internal_degree(graph, community, …) The average internal degree of the community set.
conductance(graph, community, **kwargs) Fraction of total edge volume that points outside the community.
cut_ratio(graph, community, **kwargs) Fraction of existing edges (out of all possible edges) leaving the community.
edges_inside(graph, community, **kwargs) Number of edges internal to the community.
expansion(graph, community, **kwargs) Number of edges per community node that point outside the cluster.
fraction_over_median_degree(graph, …) Fraction of community nodes of having internal degree higher than the median degree value.
internal_edge_density(graph, community, **kwargs) The internal density of the community set.
normalized_cut(graph, community, **kwargs) Normalized variant of the Cut-Ratio
max_odf(graph, community, **kwargs) Maximum fraction of edges of a node of a community that point outside the community itself.
avg_odf(graph, community, **kwargs) Average fraction of edges of a node of a community that point outside the community itself.
flake_odf(graph, community, **kwargs) Fraction of nodes in S that have fewer edges pointing inside than to the outside of the community.
significance(graph, communities, **kwargs) Significance estimates how likely a partition of dense communities appear in a random graph.
size(graph, communities, **kwargs) Size is the number of nodes in the community
surprise(graph, communities, **kwargs) Surprise is statistical approach proposes a quality metric assuming that edges between vertices emerge randomly according to a hyper-geometric distribution.
triangle_participation_ratio(graph, …) Fraction of community nodes that belong to a triad.

Among the fitness function a well-defined family of measures is the Modularity-based one:

erdos_renyi_modularity(graph, communities, …) Erdos-Renyi modularity is a variation of the Newman-Girvan one.
link_modularity(graph, communities, **kwargs) Quality function designed for directed graphs with overlapping communities.
modularity_density(graph, communities, **kwargs) The modularity density is one of several propositions that envisioned to palliate the resolution limit issue of modularity based measures.
newman_girvan_modularity(graph, communities, …) Difference the fraction of intra community edges of a partition with the expected number of such edges if distributed according to a null model.
z_modularity(graph, communities, **kwargs) Z-modularity is another variant of the standard modularity proposed to avoid the resolution limit.

Some measures will return an instance of FitnessResult that takes together min/max/mean/std values of the computed index.

FitnessResult(min, max, score, std)

Partition Comparisons

It is often useful to compare different graph partition to assess their resemblance (i.e., to perform ground truth testing). CDlib implements the following partition comparisons scores:

adjusted_mutual_information(first_partition, …) Adjusted Mutual Information between two clusterings.
adjusted_rand_index(first_partition, …) Rand index adjusted for chance.
f1(first_partition, second_partition) Compute the average F1 score of the optimal algorithms matches among the partitions in input.
nf1(first_partition, second_partition) Compute the Normalized F1 score of the optimal algorithms matches among the partitions in input.
normalized_mutual_information(…) Normalized Mutual Information between two clusterings.
omega(first_partition, second_partition) Index of resemblance for overlapping, complete coverage, network clusterings.
overlapping_normalized_mutual_information_LFK(…) Overlapping Normalized Mutual Information between two clusterings.
overlapping_normalized_mutual_information_MGH(…) Overlapping Normalized Mutual Information between two clusterings.
variation_of_information(first_partition, …) Variation of Information among two nodes partitions.

Some measures will return an instance of MatchingResult that takes together mean and standard deviation values of the computed index.

MatchingResult(score, std)