Graph Partition and Measures

Python3 code implementing 11 graph-aware measures (gam) for comparing graph partitions as well as a stable ensemble-based graph partition algorithm (ecg). This verion works with the igraph package. A version for networkx is also available: partition-networkx.

Version 0.0.8 is now compatible with igraph 1.0.0 where the semantics of the permutation argument changed.

Graph aware measures (gam)

The measures are respectively:

• 'rand': the RAND index
• 'jaccard': the Jaccard index
• 'mn': pairwise similarity normalized with the mean function
• 'gmn': pairwise similarity normalized with the geometric mean function
• 'min': pairwise similarity normalized with the minimum function
• 'max': pairwise similarity normalized with the maximum function

Each measure can be adjusted (recommended) or not, except for 'jaccard'. Details can be found in:

Valérie Poulin and François Théberge, "Comparing Graph Clusterings: Set partition measures vs. Graph-aware measures", https://arxiv.org/abs/1806.11494.

Ensemble clustering for graphs (ecg)

This is a good, stable graph partitioning algorithm. Details for ecg can be found in:

Valérie Poulin and François Théberge, "Ensemble clustering for graphs: comparisons and applications", Appl Netw Sci 4, 51 (2019). https://doi.org/10.1007/s41109-019-0162-z

Example

We need to import the supplied Python file partition_igraph.

import numpy as np
import igraph as ig
import partition_igraph

Next, let's build a graph with communities.

P = np.full((10,10),.025)
np.fill_diagonal(P,.1)
## 1000 nodes, 10 communities
g = ig.Graph.Preference(n=1000, type_dist=list(np.repeat(.1,10)),
                        pref_matrix=P.tolist(),attribute='class')
## the 'ground-truth' communities
tc = {k:v for k,v in enumerate(g.vs['class'])}

Run Louvain and ecg:

ml = g.community_multilevel()
ec = g.community_ecg(ens_size=32)

Finally, we show a few examples of measures we can compute with gam:

## for 'gam' partition are either 'igraph.clustering.VertexClustering' or 'dict'
print('Adjusted Graph-Aware Rand Index for Louvain:',g.gam(ml,tc))
print('Adjusted Graph-Aware Rand Index for ECG:',g.gam(ec,tc))
print('\nJaccard Graph-Aware for Louvain:',g.gam(ml,tc,method="jaccard",adjusted=False))
print('Jaccard Graph-Aware for ECG:',g.gam(ec,tc,method="jaccard",adjusted=False))