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Table 2.

Cluster statistics for 12 variants of four-stage clustering. All results include Stages 1 and 4, but some pipelines do not use Stages 2 or 3; all clusterings are kmp-valid. Top: results for k = 5, Bottom: results for k = 10. Stage 2 is performed using either Iterative Graclus (IG) or Recursive Graclus (RG), which are each run with either 0 or 2,000 local search iterations. Node coverage refers to the percentage of network nodes contained in nonsingleton clusters and singletons refers to the number of nodes in singleton clusters. All other statistics refer to nonsingleton clusters, with the last three columns refering to the sizes of nonsingleton clusters. Specific noteworthy trends include: (a) All clusterings that use Stage 3 have node coverage above 18%; (b) all clusterings have at least one very large cluster; (c) Stage 2 choice impacts maximum cluster size; and (d) setting k = 5 produces more clusters with a smaller median cluster size than setting k = 10.

Stage 2Stage 3Node coverageClusters (number)Singletons (number)Min.MedianMax.
k = 5 
No No 7.38% 276 13,611,485 28.0 345,139 
No Yes 36.63% 276 9,312,583 15 265.5 856,623 
IG(0) Yes 20.01% 13,709 11,752,582 118.0 19,934 
IG(2000) Yes 20.84% 9,698 11,632,959 106.0 32,487 
RG(0) Yes 26.27% 2,261 10,835,596 10 145.0 579,720 
RG(2000) Yes 26.09% 3,417 10,861,670 11 105.0 578,265 
  
k = 10 
No No 4.22% 119 14,075,787 12 85.0 213,670 
No Yes 33.69% 119 9,744,368 62 1638.0 964,503 
IG(0) Yes 18.51% 4,185 11,975,796 33 427.0 27,007 
IG(2000) Yes 20.00% 3,044 11,757,196 31 488.5 60,189 
RG(0) Yes 27.26% 359 10,689,730 67 1014.0 679,922 
RG(2000) Yes 27.61% 473 10,637,388 55 761.0 620,491 
Stage 2Stage 3Node coverageClusters (number)Singletons (number)Min.MedianMax.
k = 5 
No No 7.38% 276 13,611,485 28.0 345,139 
No Yes 36.63% 276 9,312,583 15 265.5 856,623 
IG(0) Yes 20.01% 13,709 11,752,582 118.0 19,934 
IG(2000) Yes 20.84% 9,698 11,632,959 106.0 32,487 
RG(0) Yes 26.27% 2,261 10,835,596 10 145.0 579,720 
RG(2000) Yes 26.09% 3,417 10,861,670 11 105.0 578,265 
  
k = 10 
No No 4.22% 119 14,075,787 12 85.0 213,670 
No Yes 33.69% 119 9,744,368 62 1638.0 964,503 
IG(0) Yes 18.51% 4,185 11,975,796 33 427.0 27,007 
IG(2000) Yes 20.00% 3,044 11,757,196 31 488.5 60,189 
RG(0) Yes 27.26% 359 10,689,730 67 1014.0 679,922 
RG(2000) Yes 27.61% 473 10,637,388 55 761.0 620,491 
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