Fast Convergence PageRank in MapReduce

Compute PageRank of a large scale web graph in MapReduce with Hadoop.

Overall Structure

Simple PageRank

PageRankMapper.java

keyIn:
valueIn: srcNodeId;desNodeId1,desNodeId...;
     
keyOut: srcNodeId
valueOut: NODEINFO;desNodeId1,desNodeId2...;srcOldNodePageRank;

foreach desNode:
	keyOut: desNodeId
	valueOut: NEXTPAGERANK;nextPageRank;

PageRankReducer.java

keyIn: srcNodeId
valueIn: NEXTPAGERANK;nextPageRank;
Or
valueIn: NODEINFO;desNodeId1,desNodeId2...;srcNodePageRank;

keyOut:
valueOut: srcNodeId;desNodeId1,desNodeId2...;srcNodeDegree;srcNodePageRank;

PageRankRunner.java Set the input and output path from arguments, and run the hadoop jobs for 5 iterations.

Counter.java Store the residual value in reducer in each iteraction.

Block PageRank

PageRankMapper.java

keyIn:
valueIn: uId;vId1, vId2, ...;pageRank;

KeyOut: blockId
valueOut: BE;vId;uId;NextPageRank
Or
KeyOut: blockId
valueOut: BC;vId;NextPageRank
Or
KeyOut: blockId
valueOut:NODEINFO;uId;vId1, vId2, ...;pageRank;

PageRankReducer.java

KeyIn: blockId
valueIn: BE;vId;uId;
Or
KeyIn: blockId
valueIn: BC;vId;NextPageRank
Or
KeyIn: blockId
valueIn: NODEINFO;uId;vId1, vId2, ...;pageRank;

KeyOut:
ValueOut: uId;vId1, vId2, ...;pageRank;

PageRankRunner.java Set the input and output path from arguments, and run the hadoop jobs untill the residual error becomes less than 0.001.

Counter.java Store the residual value in reducer and the number of inblock iteration in each iteraction.

Node.java Store the information of the node.

Gauss-Seidel PageRank

The java file functions are the same with the Block PageRank.

Random PageRank

The java file functions are the same with the Block PageRank.

Usage

First, run the preprocess.py script to get a pre-filtered data set. In the main method, you need to specify input and output filepaths. It will generate a file named simplepagerank_0.

The NetID used to filter out edges is hy456. Thus, rejectMin = 0.654 * 0.9 = 0.5886, rejectLimit = rejectMin + 0.01 = 0.5986. Edges actually selected in our graph is 7524427.
Then, upload the pre-filterd file simplepagerank_0 to AWS S3 bucket under path /data/.
Compile the java source code and archive classes into jar file.
```
./deploy.sh [ SimplePageRank | BlockPageRank | GaussPageRank | RandomPageRank ]
```
Clean all the compiled files and delete the existing input and output paths on S3.
```
./clean.sh [ SimplePageRank | BlockPageRank | GaussPageRank | RandomPageRank ]
```
NOTE: You need to specify your bucket_name and cluster_id in deploy.sh before executing it. Also, you need to execute clean.sh to avoid the FileAlreadyExistsException.

Results

Simple PageRank:

Average residual errors
Iteration 0 avg error 2.338487e+00
Iteration 1 avg error 3.230211e-01
Iteration 2 avg error 1.920783e-01
Iteration 3 avg error 9.410072e-02
Iteration 4 avg error 6.282157e-02

Block PageRank:

Average residual errors
Iteration 0 avg error 2.815284e+00
Iteration 1 avg error 3.809232e-02
Iteration 2 avg error 2.370591e-02
Iteration 3 avg error 9.744174e-03
Iteration 4 avg error 3.806021e-03
Iteration 5 avg error 9.442085e-04

The average number of iterations per Mapreduce per node
Iteration 0 inblock iter 17
Iteration 1 inblock iter 7
Iteration 2 inblock iter 6
Iteration 3 inblock iter 4
Iteration 4 inblock iter 3
Iteration 5 inblock iter 1

The average number of iterations per Block
block0 iter num: 7
block1 iter num: 7
block2 iter num: 12
block3 iter num: 6
block4 iter num: 8
block5 iter num: 9
block6 iter num: 7
block7 iter num: 6
block8 iter num: 8
block9 iter num: 7
block10 iter num: 11
block11 iter num: 8
block12 iter num: 5
block13 iter num: 7
block14 iter num: 3
block15 iter num: 3
block16 iter num: 3
block17 iter num: 7
block18 iter num: 7
block19 iter num: 9
block20 iter num: 12
block21 iter num: 6
block22 iter num: 7
block23 iter num: 5
block24 iter num: 6
block25 iter num: 7
block26 iter num: 8
block27 iter num: 5
block28 iter num: 10
block29 iter num: 13
block30 iter num: 13
block31 iter num: 13
block32 iter num: 18
block33 iter num: 10
block34 iter num: 9
block35 iter num: 8
block36 iter num: 7
block37 iter num: 9
block38 iter num: 7
block39 iter num: 5
block40 iter num: 6
block41 iter num: 7
block42 iter num: 9
block43 iter num: 8
block44 iter num: 4
block45 iter num: 5
block46 iter num: 7
block47 iter num: 7
block48 iter num: 7
block49 iter num: 13
block50 iter num: 6
block51 iter num: 5
block52 iter num: 11
block53 iter num: 7
block54 iter num: 5
block55 iter num: 4
block56 iter num: 4
block57 iter num: 8
block58 iter num: 5
block59 iter num: 4
block60 iter num: 6
block61 iter num: 6
block62 iter num: 6
block63 iter num: 5
block64 iter num: 5
block65 iter num: 3
block66 iter num: 6
block67 iter num: 5


The PageRank values for the two lowest-numbered Nodes in each Block
blockId:0  nodeId:0, pr:1.7662844E-5
blockId:0  nodeId:1, pr:5.3695385E-5
blockId:1  nodeId:10328, pr:4.1881407E-7
blockId:1  nodeId:10329, pr:2.4268616E-7
blockId:10  nodeId:100501, pr:7.6893843E-7
blockId:10  nodeId:100502, pr:1.1493624E-6
blockId:11  nodeId:110567, pr:0.0010613861
blockId:11  nodeId:110568, pr:9.436223E-5
blockId:12  nodeId:120945, pr:8.120434E-7
blockId:12  nodeId:120946, pr:6.764715E-7
blockId:13  nodeId:130999, pr:2.2901064E-7
blockId:13  nodeId:131000, pr:2.2901064E-7
blockId:14  nodeId:140574, pr:0.0010480268
blockId:14  nodeId:140575, pr:2.2872065E-7
blockId:15  nodeId:150953, pr:9.982691E-4
blockId:15  nodeId:150954, pr:0.0018048264
blockId:16  nodeId:161332, pr:2.2856108E-7
blockId:16  nodeId:161333, pr:2.2856108E-7
blockId:17  nodeId:171154, pr:2.2938102E-7
blockId:17  nodeId:171155, pr:2.2938102E-7
blockId:18  nodeId:181514, pr:2.2446451E-7
blockId:18  nodeId:181515, pr:7.4294576E-4
blockId:19  nodeId:191625, pr:2.593737E-4
blockId:19  nodeId:191626, pr:2.1890456E-7
blockId:2  nodeId:20373, pr:2.1890456E-7
blockId:2  nodeId:20374, pr:2.1890456E-7
blockId:20  nodeId:202004, pr:9.3714283E-7
blockId:20  nodeId:202005, pr:9.931775E-7
blockId:21  nodeId:212383, pr:0.0011738206
blockId:21  nodeId:212384, pr:2.1890456E-7
blockId:22  nodeId:222762, pr:2.2839134E-7
blockId:22  nodeId:222763, pr:2.2839134E-7
blockId:23  nodeId:232593, pr:2.3665325E-7
blockId:23  nodeId:232594, pr:2.9685523E-7
blockId:24  nodeId:242878, pr:1.0812148E-6
blockId:24  nodeId:242879, pr:5.8003235E-7
blockId:25  nodeId:252938, pr:6.115055E-6
blockId:25  nodeId:252939, pr:5.7966827E-7
blockId:26  nodeId:263149, pr:9.773459E-6
blockId:26  nodeId:263150, pr:1.7914247E-6
blockId:27  nodeId:273210, pr:2.7178543E-5
blockId:27  nodeId:273211, pr:8.344093E-7
blockId:28  nodeId:283473, pr:2.8673708E-7
blockId:28  nodeId:283474, pr:2.8673708E-7
blockId:29  nodeId:293255, pr:2.9186053E-6
blockId:29  nodeId:293256, pr:7.0410792E-6
blockId:3  nodeId:30629, pr:2.653755E-7
blockId:3  nodeId:30630, pr:2.1890456E-7
blockId:30  nodeId:303043, pr:9.99592E-7
blockId:30  nodeId:303044, pr:5.4063967E-6
blockId:31  nodeId:313370, pr:2.549086E-7
blockId:31  nodeId:313371, pr:2.3471235E-5
blockId:32  nodeId:323522, pr:5.5895447E-7
blockId:32  nodeId:323523, pr:1.3505381E-6
blockId:33  nodeId:333883, pr:1.8997793E-5
blockId:33  nodeId:333884, pr:4.294905E-6
blockId:34  nodeId:343663, pr:2.12809E-6
blockId:34  nodeId:343664, pr:3.6849823E-7
blockId:35  nodeId:353645, pr:1.974418E-6
blockId:35  nodeId:353646, pr:9.506203E-7
blockId:36  nodeId:363929, pr:1.4328717E-5
blockId:36  nodeId:363930, pr:4.5782957E-7
blockId:37  nodeId:374236, pr:2.3927763E-7
blockId:37  nodeId:374237, pr:1.02101285E-5
blockId:38  nodeId:384554, pr:6.639836E-5
blockId:38  nodeId:384555, pr:5.353761E-6
blockId:39  nodeId:394929, pr:3.9610222E-6
blockId:39  nodeId:394930, pr:2.6018472E-6
blockId:4  nodeId:40645, pr:2.4612109E-5
blockId:4  nodeId:40646, pr:2.4612109E-5
blockId:40  nodeId:404712, pr:7.101309E-7
blockId:40  nodeId:404713, pr:8.2066214E-7
blockId:41  nodeId:414617, pr:3.7004725E-7
blockId:41  nodeId:414618, pr:3.7004725E-7
blockId:42  nodeId:424747, pr:1.0904894E-6
blockId:42  nodeId:424748, pr:3.633363E-6
blockId:43  nodeId:434707, pr:5.1756234E-7
blockId:43  nodeId:434708, pr:3.1663199E-6
blockId:44  nodeId:444489, pr:4.922495E-7
blockId:44  nodeId:444490, pr:2.396862E-7
blockId:45  nodeId:454285, pr:3.502824E-7
blockId:45  nodeId:454286, pr:3.1814386E-7
blockId:46  nodeId:464398, pr:5.291867E-7
blockId:46  nodeId:464399, pr:5.291867E-7
blockId:47  nodeId:474196, pr:5.194032E-7
blockId:47  nodeId:474197, pr:8.366151E-7
blockId:48  nodeId:484050, pr:1.6480262E-5
blockId:48  nodeId:484051, pr:1.2461775E-5
blockId:49  nodeId:493968, pr:8.240514E-7
blockId:49  nodeId:493969, pr:1.3858079E-6
blockId:5  nodeId:50462, pr:0.0049371514
blockId:5  nodeId:50463, pr:0.005076542
blockId:50  nodeId:503752, pr:7.909762E-7
blockId:50  nodeId:503753, pr:7.909762E-7
blockId:51  nodeId:514131, pr:0.0011306099
blockId:51  nodeId:514132, pr:2.6927848E-5
blockId:52  nodeId:524510, pr:8.431597E-4
blockId:52  nodeId:524511, pr:1.3700465E-5
blockId:53  nodeId:534709, pr:0.009103795
blockId:53  nodeId:534710, pr:4.1387407E-6
blockId:54  nodeId:545088, pr:0.001760785
blockId:54  nodeId:545089, pr:3.3292647E-5
blockId:55  nodeId:555467, pr:0.0017870528
blockId:55  nodeId:555468, pr:7.783612E-7
blockId:56  nodeId:565846, pr:2.1890456E-7
blockId:56  nodeId:565847, pr:2.1890456E-7
blockId:57  nodeId:576225, pr:1.18927155E-5
blockId:57  nodeId:576226, pr:2.1890456E-7
blockId:58  nodeId:586604, pr:3.8985116E-4
blockId:58  nodeId:586605, pr:2.989422E-7
blockId:59  nodeId:596585, pr:1.3329229E-6
blockId:59  nodeId:596586, pr:1.3862228E-6
blockId:6  nodeId:60841, pr:1.1812559E-5
blockId:6  nodeId:60842, pr:3.0127403E-6
blockId:60  nodeId:606367, pr:3.1642938E-7
blockId:60  nodeId:606368, pr:2.249009E-7
blockId:61  nodeId:616148, pr:7.955278E-7
blockId:61  nodeId:616149, pr:4.2555445E-7
blockId:62  nodeId:626448, pr:2.1890456E-7
blockId:62  nodeId:626449, pr:2.583953E-7
blockId:63  nodeId:636240, pr:2.2849078E-7
blockId:63  nodeId:636241, pr:2.2901064E-7
blockId:64  nodeId:646022, pr:5.682022E-7
blockId:64  nodeId:646023, pr:4.1093793E-7
blockId:65  nodeId:655804, pr:2.2849078E-7
blockId:65  nodeId:655805, pr:2.1890456E-7
blockId:66  nodeId:665666, pr:2.5611834E-7
blockId:66  nodeId:665667, pr:4.024848E-7
blockId:67  nodeId:675448, pr:2.1890456E-7
blockId:67  nodeId:675449, pr:4.9050273E-6
blockId:7  nodeId:70591, pr:2.4612109E-5
blockId:7  nodeId:70592, pr:2.4612109E-5
blockId:8  nodeId:80118, pr:5.3006863E-7
blockId:8  nodeId:80119, pr:9.80627E-7
blockId:9  nodeId:90497, pr:9.155742E-7
blockId:9  nodeId:90498, pr:1.1305711E-5

Gauss PageRank

Average residual errors
Iteration 0 avg error 5.553232e+00
Iteration 1 avg error 2.642470e-02
Iteration 2 avg error 7.954993e-03
Iteration 3 avg error 3.118661e-03
Iteration 4 avg error 1.259431e-03
Iteration 5 avg error 3.867315e-04

The average number of iterations per Mapreduce per node
Iteration 0 inblock iter 2
Iteration 1 inblock iter 2
Iteration 2 inblock iter 2
Iteration 3 inblock iter 2
Iteration 4 inblock iter 1
Iteration 5 inblock iter 1

The average number of iterations per Block
block0 iter num: 2
block1 iter num: 1
block2 iter num: 2
block3 iter num: 1
block4 iter num: 2
block5 iter num: 1
block6 iter num: 2
block7 iter num: 2
block8 iter num: 2
block9 iter num: 2
block10 iter num: 2
block11 iter num: 2
block12 iter num: 2
block13 iter num: 2
block14 iter num: 1
block15 iter num: 1
block16 iter num: 1
block17 iter num: 2
block18 iter num: 2
block19 iter num: 2
block20 iter num: 2
block21 iter num: 2
block22 iter num: 2
block23 iter num: 1
block24 iter num: 1
block25 iter num: 2
block26 iter num: 2
block27 iter num: 2
block28 iter num: 2
block29 iter num: 2
block30 iter num: 2
block31 iter num: 2
block32 iter num: 2
block33 iter num: 2
block34 iter num: 1
block35 iter num: 1
block36 iter num: 1
block37 iter num: 1
block38 iter num: 1
block39 iter num: 1
block40 iter num: 1
block41 iter num: 2
block42 iter num: 2
block43 iter num: 2
block44 iter num: 1
block45 iter num: 1
block46 iter num: 2
block47 iter num: 2
block48 iter num: 2
block49 iter num: 2
block50 iter num: 2
block51 iter num: 1
block52 iter num: 2
block53 iter num: 2
block54 iter num: 1
block55 iter num: 2
block56 iter num: 1
block57 iter num: 2
block58 iter num: 1
block59 iter num: 2
block60 iter num: 2
block61 iter num: 2
block62 iter num: 1
block63 iter num: 1
block64 iter num: 1
block65 iter num: 1
block66 iter num: 2
block67 iter num: 1


The PageRank values for the two lowest-numbered Nodes in each Block
blockId:0  nodeId:0, pr:2.6917796E-6
blockId:0  nodeId:1, pr:3.3014796E-6
blockId:1  nodeId:10328, pr:2.955301E-7
blockId:1  nodeId:10329, pr:2.1890456E-7
blockId:10  nodeId:100501, pr:2.1890456E-7
blockId:10  nodeId:100502, pr:2.1890456E-7
blockId:11  nodeId:110567, pr:1.21030804E-4
blockId:11  nodeId:110568, pr:2.1890456E-7
blockId:12  nodeId:120945, pr:2.1890456E-7
blockId:12  nodeId:120946, pr:2.1890456E-7
blockId:13  nodeId:130999, pr:2.2454302E-7
blockId:13  nodeId:131000, pr:2.2454302E-7
blockId:14  nodeId:140574, pr:5.420391E-4
blockId:14  nodeId:140575, pr:2.2437717E-7
blockId:15  nodeId:150953, pr:5.1592133E-4
blockId:15  nodeId:150954, pr:7.453649E-4
blockId:16  nodeId:161332, pr:2.1890456E-7
blockId:16  nodeId:161333, pr:2.1890456E-7
blockId:17  nodeId:171154, pr:2.1890456E-7
blockId:17  nodeId:171155, pr:2.1890456E-7
blockId:18  nodeId:181514, pr:2.2344283E-7
blockId:18  nodeId:181515, pr:2.1890456E-7
blockId:19  nodeId:191625, pr:8.663219E-6
blockId:19  nodeId:191626, pr:2.1890456E-7
blockId:2  nodeId:20373, pr:2.1890456E-7
blockId:2  nodeId:20374, pr:2.1890456E-7
blockId:20  nodeId:202004, pr:2.1890456E-7
blockId:20  nodeId:202005, pr:2.1890456E-7
blockId:21  nodeId:212383, pr:2.0140444E-5
blockId:21  nodeId:212384, pr:2.1890456E-7
blockId:22  nodeId:222762, pr:2.1890456E-7
blockId:22  nodeId:222763, pr:2.1890456E-7
blockId:23  nodeId:232593, pr:2.1890456E-7
blockId:23  nodeId:232594, pr:2.1890456E-7
blockId:24  nodeId:242878, pr:3.1470552E-7
blockId:24  nodeId:242879, pr:2.1890456E-7
blockId:25  nodeId:252938, pr:2.1890456E-7
blockId:25  nodeId:252939, pr:2.1890456E-7
blockId:26  nodeId:263149, pr:2.6215673E-6
blockId:26  nodeId:263150, pr:2.1890456E-7
blockId:27  nodeId:273210, pr:2.1890456E-7
blockId:27  nodeId:273211, pr:2.1890456E-7
blockId:28  nodeId:283473, pr:2.1890456E-7
blockId:28  nodeId:283474, pr:2.1890456E-7
blockId:29  nodeId:293255, pr:2.3797355E-7
blockId:29  nodeId:293256, pr:2.1890456E-7
blockId:3  nodeId:30629, pr:2.2634731E-7
blockId:3  nodeId:30630, pr:2.1890456E-7
blockId:30  nodeId:303043, pr:2.2667437E-7
blockId:30  nodeId:303044, pr:9.3640386E-7
blockId:31  nodeId:313370, pr:2.4991604E-7
blockId:31  nodeId:313371, pr:2.4492435E-6
blockId:32  nodeId:323522, pr:2.3581991E-7
blockId:32  nodeId:323523, pr:2.8908522E-7
blockId:33  nodeId:333883, pr:1.2511396E-6
blockId:33  nodeId:333884, pr:2.1890456E-7
blockId:34  nodeId:343663, pr:3.8330973E-7
blockId:34  nodeId:343664, pr:2.680799E-7
blockId:35  nodeId:353645, pr:3.4110846E-7
blockId:35  nodeId:353646, pr:2.1890456E-7
blockId:36  nodeId:363929, pr:7.4048086E-7
blockId:36  nodeId:363930, pr:2.5743992E-7
blockId:37  nodeId:374236, pr:2.3751144E-7
blockId:37  nodeId:374237, pr:2.1890456E-7
blockId:38  nodeId:384554, pr:2.730834E-6
blockId:38  nodeId:384555, pr:2.1890456E-7
blockId:39  nodeId:394929, pr:2.3921274E-7
blockId:39  nodeId:394930, pr:2.6245544E-7
blockId:4  nodeId:40645, pr:8.711444E-6
blockId:4  nodeId:40646, pr:8.711444E-6
blockId:40  nodeId:404712, pr:2.809275E-7
blockId:40  nodeId:404713, pr:2.1890456E-7
blockId:41  nodeId:414617, pr:2.1890456E-7
blockId:41  nodeId:414618, pr:2.1890456E-7
blockId:42  nodeId:424747, pr:2.1890456E-7
blockId:42  nodeId:424748, pr:2.1890456E-7
blockId:43  nodeId:434707, pr:2.1890456E-7
blockId:43  nodeId:434708, pr:2.8137038E-7
blockId:44  nodeId:444489, pr:2.5609503E-7
blockId:44  nodeId:444490, pr:2.1890456E-7
blockId:45  nodeId:454285, pr:2.664664E-7
blockId:45  nodeId:454286, pr:2.1890456E-7
blockId:46  nodeId:464398, pr:2.9664838E-7
blockId:46  nodeId:464399, pr:2.9664838E-7
blockId:47  nodeId:474196, pr:2.8486392E-7
blockId:47  nodeId:474197, pr:2.1890456E-7
blockId:48  nodeId:484050, pr:1.974814E-6
blockId:48  nodeId:484051, pr:2.1890456E-7
blockId:49  nodeId:493968, pr:2.3772532E-7
blockId:49  nodeId:493969, pr:4.3155472E-7
blockId:5  nodeId:50462, pr:0.0017778346
blockId:5  nodeId:50463, pr:0.001789626
blockId:50  nodeId:503752, pr:2.1890456E-7
blockId:50  nodeId:503753, pr:2.1890456E-7
blockId:51  nodeId:514131, pr:1.7408875E-4
blockId:51  nodeId:514132, pr:2.1890456E-7
blockId:52  nodeId:524510, pr:2.383244E-5
blockId:52  nodeId:524511, pr:2.1890456E-7
blockId:53  nodeId:534709, pr:0.0014140059
blockId:53  nodeId:534710, pr:9.058025E-7
blockId:54  nodeId:545088, pr:1.5198407E-4
blockId:54  nodeId:545089, pr:2.1890456E-7
blockId:55  nodeId:555467, pr:2.4756152E-4
blockId:55  nodeId:555468, pr:2.462755E-7
blockId:56  nodeId:565846, pr:2.1890456E-7
blockId:56  nodeId:565847, pr:2.1890456E-7
blockId:57  nodeId:576225, pr:2.3785208E-6
blockId:57  nodeId:576226, pr:2.1890456E-7
blockId:58  nodeId:586604, pr:3.5366572E-6
blockId:58  nodeId:586605, pr:2.2076524E-7
blockId:59  nodeId:596585, pr:2.1890456E-7
blockId:59  nodeId:596586, pr:2.1890456E-7
blockId:6  nodeId:60841, pr:8.4031893E-7
blockId:6  nodeId:60842, pr:2.1890456E-7
blockId:60  nodeId:606367, pr:2.552269E-7
blockId:60  nodeId:606368, pr:2.1890456E-7
blockId:61  nodeId:616148, pr:2.5062084E-7
blockId:61  nodeId:616149, pr:2.1890456E-7
blockId:62  nodeId:626448, pr:2.1890456E-7
blockId:62  nodeId:626449, pr:2.1890456E-7
blockId:63  nodeId:636240, pr:2.2422081E-7
blockId:63  nodeId:636241, pr:2.2454302E-7
blockId:64  nodeId:646022, pr:2.1890456E-7
blockId:64  nodeId:646023, pr:2.1890456E-7
blockId:65  nodeId:655804, pr:2.2422081E-7
blockId:65  nodeId:655805, pr:2.1890456E-7
blockId:66  nodeId:665666, pr:2.5611834E-7
blockId:66  nodeId:665667, pr:2.2323174E-7
blockId:67  nodeId:675448, pr:2.1890456E-7
blockId:67  nodeId:675449, pr:2.1890456E-7
blockId:7  nodeId:70591, pr:8.711444E-6
blockId:7  nodeId:70592, pr:8.711444E-6
blockId:8  nodeId:80118, pr:2.1890456E-7
blockId:8  nodeId:80119, pr:2.1890456E-7
blockId:9  nodeId:90497, pr:2.1890456E-7
blockId:9  nodeId:90498, pr:9.941915E-7

Random PageRank:

Average residual error
Iteration 0 avg error 2.327331e+00
Iteration 1 avg error 3.221458e-01
Iteration 2 avg error 1.906236e-01
Iteration 3 avg error 9.294543e-02
Iteration 4 avg error 6.163624e-02
Iteration 5 avg error 3.319469e-02
Iteration 6 avg error 2.640865e-02
Iteration 7 avg error 1.614786e-02

yhfyhf / Fast-Convergence-PageRank-in-MapReduce