Fig 1.
The 8×8 lattice on the right and its line graph on the left.
4 clusters are highlighted by the rectangles with corresponding colours. The medoids on the line graph are presented by big circles, while in the original graph medoids are identified by bold edges.
Table 1.
Basic statistics of the networks used in the computational experiments.
Table 2.
Comparison exact and heuristic versions of the LPAM method in terms of ONMI.
Table 3.
Time efforts for exact version of LPAM method in comparision with heuristic.
Table 4.
F1 median score results table.
Maximum values are highlighted by green backgound.
Table 5.
Maximum values are highlighted by green backgound.
Table 6.
Median values of overlapping normalized mutual information (LFK).
Maximum values are highlighted by green backgound.
Table 7.
Maximum values are highlighted by green backgound.
Table 8.
Maximum values of omega index for each clustering method.
Maximum values are highlighted by green backgound.
Table 9.
Maximum values of overlapping normalized mutual information (LFK) producced by clustering algorithms.
Maximum values in a row are highlighted by green backgound.
Table 10.
Median values of internal cluster edge density.
Maximum values are highlighted by green backgound.
Table 11.
Maximux Internal cluster edge density median.
Maximum values are highlighted by green backgound.
Table 12.
Median values of normalized cut.
Maximum values are highlighted by green backgound.
Table 13.
Minimum values of normalized cut produced by a method.
Minimum values are highlighted by green backgound.
Table 14.
The average execution time(seconds).
Minimum values are highlighted by green backgound.
Table 15.
Maximum values of time execution (seconds).
Minimum values are highlighted by green backgound.
Fig 2.
Clustering results of the exact version of the LPAM method with amplified commute distance for the School Friendship network.
θ = 0.5, k = 7. The paired numbers, separated by a colon inside the nodes, denote the predicted ID of the cluster provided by the LPAM method and the node attribute, respectively. In addition, the LPAM algorithm covering are denoted by colors. As seen in the picture, the algorithm correctly revealed community 3, 5, and 6. Also, the algorithm does not assign the nodes that have connections with more than two clusters, to any cluster. That is because of the parameter θ = 0.5 The LPAM method falsely separates community 4 into two clusters (4—yellow and 3—purple). Moreover, the algorithm almost correctly identifies the small community 1 (green); however, it incorrectly assigns the node from community 2 to this cluster.
Fig 3.
A line graph which is produced by the exact version of the LPAM method with amplified commute distance for the School Friendship network (θ = 0.5, k = 7).
Fig 4.
The ONMI results for the exact version of the LPAM method with amplified commute distance depending on the threshold parameter θ.
Fig 5.
The clustering results of the heuristic version of the LPAM method with amplified commute distance for the FARZ networks with 200 nodes and 5 communities.
(a) β = 1, (b) β = 0.95, (c) β = 0.9, (d) β = 0.85, (e) β = 0.8, (f) β = 0.75, (g) β = 0.7, (h) β = 0.65, (i) β = 0.6, (j) β = 0.55, (k) β = 0.5.