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Table 5 Network statistics (a), wall clock running times (b), and throughput (c) pertinent to scalability of VCP algorithms

From: Vertex collocation profiles: theory, computation, and results

(a) Network statistics

Name

Vertices

Edges

Density

â„“ =2 Pairs

calls

7,786,471

33,292,508

5.49×10−7

2.46×108

condmat

17,216

110,544

7.46×10−4

3.80×105

dblp-cite

15,963

344,373

1.35×10−3

1.97×107

dblp-collab

367,725

2,088,710

3.09×10−5

1.07×107

disease-g

399

15,634

1.97×10−1

5.87×104

disease-p

437

81,158

8.52×10−1

5.46×104

hepth-cite

8,249

335,028

4.92×10−3

1.23×107

hepth-collab

8,381

40,736

1.16×10−3

1.45×105

huddle

4,243

997,008

1.11×10−1

7.29×106

patents-collab

1,162,227

5,448,168

8.07×10−6

2.50×107

sms

5,016,746

11,598,843

4.61×10−7

4.74×107

(b) Wall clock running times (in seconds)

Name

VCP 3,1,0

VCP 3,1,1

VCP 4,1,0

VCP 4,1,1

calls

85.0

531.2

2660.0

3763.0

condmat

0.1

-

2.6

-

dblp-cite

23.9

120.8

11561.7

19686.6

dblp-collab

2.7

-

149.3

-

disease-g

0.1

-

2.3

-

disease-p

0.1

-

13.9

-

hepth-cite

25.0

125.4

12830.1

24818.7

hepth-collab

0.1

-

0.8

-

huddle

17.4

-

14360.3

-

patents-collab

7.7

-

462.3

-

sms

10.7

66.1

177.6

242.5

(c) Throughput (pairs per second)

Name

VCP 3,1,0

VCP 3,1,1

VCP 4,1,0

VCP 4,1,1

calls

2.9×106

4.6×105

9.3×104

6.5×104

condmat

5.0×106

-

1.4×105

-

dblp-cite

8.2×105

1.6×105

1.7×103

1.0×103

dblp-collab

3.9×106

-

7.1×104

-

disease-g

2.0×106

-

2.6×104

-

disease-p

6.7×105

-

3.9×103

-

hepth-cite

4.9×105

9.9×104

9.6×102

5.0×102

hepth-collab

4.8×106

-

1.8×105

-

huddle

4.2×105

-

5.1×102

-

patents-collab

3.3×106

-

5.3×104

-

sms

4.4×106

7.2×105

2.6×105

1.9×105

  1. Density is reported as 2 | E | | V | ( | V | − 1 ) in undirected networks and | E | | V | ( | V | − 1 ) in directed networks. Stated running times and throughputs are the arithmetic mean of 10 runs, but variances are negligible.