Implementation of the PageRank algorithm
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README.md

WARNING

This is NOT a complete, nor even a very good, PageRank implementation. This was a learning implementation and, as such, should be treated as a simple learning project. Use at your own risk.

PageRank

Timothy Asp (@timothyasp)

Caleb Carlton (@ccarlton)

Run Instructions:

NOTE: NetworkX is required for installation. Run sudo easy_install networkx

For directed data, run: python pageRank.py directed For undirected data, run: python pageRank.py undirected

Implementation

Generates a directed or undirected graph of the data, then runs the PageRank algorithm, iterating over every node checking the neighbors (undirected) and out-edges (directed). We used NetworkX (http://networkx.lanl.gov/) for out graphs which is a great python library for creating and maintaining these graphs. For D, which is the probability that the user will randomly go to a different page, we chose .85 which is what the book had as the probability for D. The graph is iterated over 10 times, to calculate the rank best.

State Borders

Analysis: The top ranked states are all high density area states, meaning they have lots of state borders, which makes sense and matches expected output.

   MO                             :0.0315971844476
   KY                             :0.0311331684216
   TN                             :0.0310935756102
   MA                             :0.0287725140929
   PA                             :0.0269173607527
   MD                             :0.0267222576413
   GA                             :0.0262810787353
   NY                             :0.0261652680999
   SD                             :0.0259332059378
   WY                             :0.0256935355929
   IA                             :0.0255032593163
   CO                             :0.0252932994762
   VA                             :0.0250814382815
   ID                             :0.0250734427792
   AR                             :0.023278072507
   OK                             :0.0223321781313
   NV                             :0.0216708088742
   NB                             :0.0214511655309
   NE                             :0.0214511655309
   OH                             :0.021122132435
   WV                             :0.02097603798
   TX                             :0.0203753104517
   NH                             :0.0203612457806
   UT                             :0.0201041909315
   IL                             :0.0194874330536
   OR                             :0.0186831020097
   KS                             :0.0182382396929
   AL                             :0.0180729949833
   VT                             :0.0180524967929
   NC                             :0.017964064708
   CT                             :0.0177488522188
   AZ                             :0.0175795169308
   MS                             :0.0171642829093
   IN                             :0.0170252621532
   WI                             :0.0167143241873
   MT                             :0.0164648690288
   MN                             :0.0164414868817
   NM                             :0.0163676118695
   NJ                             :0.0154237955317
   DE                             :0.0149027237957
   CA                             :0.014328872014
   MI                             :0.0137016010819
   LA                             :0.0133453258507
   ND                             :0.0130759232999
   RI                             :0.0128664771188
   FL                             :0.0104997265484
   SC                             :0.0104816930419
   WA                             :0.0104611056458
   DC                             :0.0102730766081
   MV                             :0.0100317563706
   ME                             :0.00871019610841

Political Blogs

   855                            :0.0123982365159
   155                            :0.0102073178341
   963                            :0.0085996555082
   1051                           :0.00779787367556
   641                            :0.00740159936356
   55                             :0.00708484611118
   1245                           :0.0059611211307
   1153                           :0.00569707706033
   1437                           :0.00562599374973
   729                            :0.00547134446998
   1112                           :0.00527363212751
   1479                           :0.00487418572979
   1041                           :0.00469773070457
   454                            :0.00469567338062
   1101                           :0.00464578664097
   363                            :0.00447834018621
   323                            :0.00435790083927
   1000                           :0.0038614062333
   798                            :0.00381999172434
   642                            :0.00370102086354
   741                            :0.0036547261639
   979                            :0.00362174829003
   434                            :0.0036180870679
   1179                           :0.00350056696695
   493                            :0.00346775923273
   512                            :0.0034349511101
   880                            :0.00342661996956
   180                            :0.00341641339595
   996                            :0.00340638815647
   1270                           :0.00340087077945
   387                            :0.00339655223689
   1461                           :0.00332533847476
   878                            :0.00324778609618
   756                            :0.0032359049905
   1306                           :0.00315517498621
   144                            :0.00312457924806
   483                            :0.00309610699993
   535                            :0.00308475291018
   99                             :0.00307278802084
   1330                           :0.00301907244338
   189                            :0.00301478979974
   1209                           :0.00300901159605
   980                            :0.00299508763393
   170                            :0.00298107564567
   1463                           :0.00283380952926
   762                            :0.00280848085965
   856                            :0.00279802241224
   644                            :0.00276932320703
   1384                           :0.00276752568959
   547                            :0.0027426663457
   514                            :0.00273565583007
   72                             :0.00273238941209
   919                            :0.00273076502953
   664                            :0.00272610535733
   687                            :0.00270819350753
   150                            :0.00269966673637
   524                            :0.00268026659323
   826                            :0.00266091439199
   119                            :0.00265691688035
   297                            :0.00264045909771
   935                            :0.00263408868513
   892                            :0.00261845274543
   … trimmed

NCAA

Analysis: A quick look through the 2009 season results show that most of the teams ranked the highest we’re the division leaders and winning teams.

   Boise State                    :0.00733262361219
   Utah                           :0.00722435930833
   Montana                        :0.00709947017054
   Tulsa                          :0.00670055195551
   Ball State                     :0.0063758368291
   Texas                          :0.00636546801443
   Rice                           :0.00636420852951
   Alabama                        :0.00625447664103
   Florida                        :0.00624166939591
   TCU                            :0.00612222447911
   Texas Tech                     :0.00602273860572
   Penn State                     :0.00583129342948
   Cincinnati                     :0.00575753270947
   Oklahoma                       :0.0056904527237
   Richmond                       :0.00547645775694
   East Carolina                  :0.00529388406925
   Missouri                       :0.00524749922454
   Ohio State                     :0.00522310227913
   Brigham Young                  :0.00514457541395
   Weber State                    :0.00513022880521
   Nebraska                       :0.00504668897937
   USC                            :0.00499134298746
   New Hampshire                  :0.00498805759706
   Georgia                        :0.00496366497189
   Michigan State                 :0.00492355290029
   Iowa                           :0.00491360116607
   Western Michigan               :0.00488826180424
   James Madison                  :0.00488409341977
   Houston                        :0.00487147333886
   Northwestern                   :0.00485804367807
   Troy                           :0.00481302701871
   Pittsburgh                     :0.00480537805717
   Louisiana Tech                 :0.00476687389604
   Air Force                      :0.00472795714934
   Oklahoma State                 :0.00472453412691
   Buffalo                        :0.00469183049703
   West Virginia                  :0.00468412914986
   Virginia Tech                  :0.00467792833048
   Villanova                      :0.00461018702304
   Mississippi                    :0.00460722692705
   LSU                            :0.00458586681751
   South Carolina State           :0.00457632203178
   Navy                           :0.00455469420055
   Oregon                         :0.00455031908469
   Boston College                 :0.00453703396878
   Fresno State                   :0.00444681070456
   Rutgers                        :0.00440682553538
   Florida Atlantic               :0.00439888351631
   Connecticut                    :0.00437901660454
   Florida A&M                    :0.00437700673944
   Kansas                         :0.00437053073582
   Southern Miss                  :0.00434165382392
   Colorado State                 :0.00433892942647
   Nevada                         :0.00432803496027
   South Florida                  :0.00431247388258
   Florida State                  :0.00430781518633
   Appalachian State              :0.0042855078864
   Maine                          :0.00427719960866
   San Jose State                 :0.00421017077414
   Georgia Tech                   :0.00417210375934
   Central Michigan               :0.00416730758325
   Wake Forest                    :0.00404176127288
   Minnesota                      :0.00399261481722
   Bethune-Cookman                :0.00395345951099
   Louisiana-Lafayette            :0.00394932125891
   Montana State                  :0.00392668285699
   California                     :0.0038692041512
   Wisconsin                      :0.00385875981679
   Memphis                        :0.00382804688824
   Maryland                       :0.00380882019124
   North Carolina                 :0.0038077233882
   Notre Dame                     :0.00380022455306
   Kentucky                       :0.0037939751987
   Vanderbilt                     :0.00378971204221
   Arizona                        :0.0037893865312
   Oregon State                   :0.00377213824036
   Cal Poly                       :0.00374115053075
   Hawaii                         :0.0037386301266
   Eastern Washington             :0.00369986078233
   South Carolina                 :0.00366865310273
   Arkansas State                 :0.0036312635554
   Wofford                        :0.00362089389909
   Miami (FL)                     :0.00361898361937
   Northern Arizona               :0.00356914337631
   Bowling Green                  :0.00355155219836
   UTEP                           :0.0034868669963
   William & Mary                 :0.00345594533534
   Colgate                        :0.00343346141159
   Northern Iowa                  :0.00341207809157
   Clemson                        :0.00340172846317
   Central Arkansas               :0.00339275926671
   Kansas State                   :0.00336454093013
   Florida International          :0.00330978664396
   Elon                           :0.00330964240795
   Morgan State                   :0.00329645553639
   Harvard                        :0.00324203805793
   Grambling State                :0.00319995545647

Les Miserables

Analysis: The main characters are ranked the highest, which is as expected

    Valjean                        :0.0758308901974
    Myriel                         :0.0429505779458
    Gavroche                       :0.0359160666477
    Marius                         :0.0310172618335
    Javert                         :0.0304815194381
    Thenardier                     :0.0280510981415
    Fantine                        :0.027191326266
    Enjolras                       :0.0219890272928
    Cosette                        :0.0207014337229
    MmeThenardier                  :0.0196084909871
    Bossuet                        :0.0190434224611
    Courfeyrac                     :0.0186615760305
    Eponine                        :0.0178862752016
    Mabeuf                         :0.0175458955297
    Joly                           :0.0172827540076
    Bahorel                        :0.0172689775792
    Babet                          :0.0167910676219
    Gueulemer                      :0.0167728629274
    Claquesous                     :0.0166377902786
    MlleGillenormand               :0.0163128064923
    Feuilly                        :0.0159647347833
    Combeferre                     :0.0159634323963
    Tholomyes                      :0.0157308656902
    Bamatabois                     :0.0156663859666
    Montparnasse                   :0.0152477377714
    Gillenormand                   :0.0150159848507
    Grantaire                      :0.014524331992
    Prouvaire                      :0.0131993961441
    Favourite                      :0.0126897550776
    Fameuil                        :0.0126870828847
    Dahlia                         :0.0126820677133
    Blacheville                    :0.0126796581368
    Zephine                        :0.0126773324066
    Listolier                      :0.0126750883243
    Cochepaille                    :0.0125074398829
    Chenildieu                     :0.0125030179402
    Judge                          :0.0124920149995
    Champmathieu                   :0.0124884594437
    Brevet                         :0.0124851057688
    Brujon                         :0.0119298962133
    Fauchelevent                   :0.0116775047428
    MmeHucheloup                   :0.0107290724039
    MlleBaptistine                 :0.0103332200281
    MmeMagloire                    :0.0103247490448
    Simplice                       :0.00911030673281
    LtGillenormand                 :0.00874898560852
    MmeBurgon                      :0.00782036048117
    Pontmercy                      :0.0073937575872
    Toussaint                      :0.00686488659601
    Woman2                         :0.00686488659601
    Anzelma                        :0.00633806764306
    MotherInnocent                 :0.00621997328001
    MmePontmercy                   :0.00602616566625
    Child1                         :0.0058066429878
    Child2                         :0.00580537558791
    Champtercier                   :0.00560655179602
    Geborand                       :0.00560655179602
    Napoleon                       :0.00560655179602
    Count                          :0.00560655179602
    OldMan                         :0.00559885107345
    Cravatte                       :0.00559885107345
    CountessDeLo                   :0.00559885107345
    Perpetue                       :0.00542796568708
    Magnon                         :0.00528924458944
    Marguerite                     :0.0052793453439
    Jondrette                      :0.00527170515255
    Woman1                         :0.00526257949406
    BaronessT                      :0.00516084129531
    Gribier                        :0.0044295217059
    MlleVaubois                    :0.00393126768321
    Scaufflaire                    :0.00373850352216
    Labarre                        :0.00373850352216
    Isabeau                        :0.00373850352216
    Gervais                        :0.00373850352216
    MmeDeR                         :0.00373850352216
    Boulatruelle                   :0.00343826653682
    MotherPlutarch                 :0.00330387114808

Karate

Analysis: Looking through the data, the top people the most connections, thus making them the highest ranked, so it’s as expected

    34                             :0.100779659381
    1                              :0.097005456951
    33                             :0.071576888392
    3                              :0.0570213307483
    2                              :0.0528547897183
    32                             :0.037117301531
    4                              :0.0358484502685
    24                             :0.0314579138303
    9                              :0.0297284975846
    14                             :0.0295173382004
    7                              :0.0291367362044
    6                              :0.0291334696727
    30                             :0.0262477118839
    28                             :0.0256009815829
    31                             :0.0245624539154
    8                              :0.0244823644259
    5                              :0.0219971434271
    11                             :0.0219885658829
    25                             :0.0210407262397
    26                             :0.0209763705902
    20                             :0.0195946521061
    29                             :0.0195468185624
    17                             :0.0167941834548
    27                             :0.0150190551952
    13                             :0.0146437100611
    22                             :0.0145596783316
    18                             :0.0145570208576
    19                             :0.0145207772694
    21                             :0.0145118570135
    23                             :0.0145118570135
    15                             :0.0145118570135
    16                             :0.0145118570135
    10                             :0.014293551594
    12                             :0.0095651796064

Dolphins

    Grin                           :0.032098769619
    Jet                            :0.0318806892333
    Trigger                        :0.0312662964391
    Web                            :0.0302903715199
    SN4                            :0.0298427560105
    Topless                        :0.0294801891168
    Scabs                          :0.0283966864331
    Patchback                      :0.0264319121028
    Gallatin                       :0.0263223854408
    Beescratch                     :0.0247553683412
    Kringel                        :0.0246260790508
    SN63                           :0.0239144788977
    Feather                        :0.0235998207139
    SN9                            :0.0219581962847
    Upbang                         :0.0217432490668
    Stripes                        :0.0216651111975
    SN100                          :0.0206241003106
    DN21                           :0.0201591774591
    Haecksel                       :0.019855361239
    Jonah                          :0.0193677489256
    TR99                           :0.019209987275
    SN96                           :0.0176136632619
    TR77                           :0.0173381999006
    Number1                        :0.0171934420037
    Double                         :0.0170864915312
    Beak                           :0.0169533238355
    MN105                          :0.0169216400508
    MN83                           :0.0168828868947
    Hook                           :0.0166108587996
    SN90                           :0.0162182764868
    Shmuddel                       :0.015898717753
    DN63                           :0.0156906891579
    PL                             :0.0153202288699
    Fish                           :0.0150996337083
    Oscar                          :0.0148566792738
    Zap                            :0.0147590831571
    DN16                           :0.0145192871451
    Ripplefluke                    :0.0133626577398
    Bumper                         :0.0133280233838
    Knit                           :0.0129680844496
    Thumper                        :0.0128173211756
    TSN103                         :0.0120603851553
    Mus                            :0.0115560295913
    Notch                          :0.0112467062498
    Zipfel                         :0.0110318043671
    MN60                           :0.00985621187565
    CCL                            :0.00962034429327
    TR88                           :0.00887000341
    TR120                          :0.00881850953712
    Wave                           :0.00836058683041
    TSN83                          :0.00817461979539
    SN89                           :0.00778446718663
    Vau                            :0.00748623884361
    Zig                            :0.00620544119831
    Quasi                          :0.0054370288389
    MN23                           :0.00543030882186
    TR82                           :0.00528011214892
    Cross                          :0.00507523069316
    Five                           :0.00507523069316
    Whitetip                       :0.0049602682216
    SMN5                           :0.00491419391454
    Fork                           :0.00483181375568

Conclusion

PageRank worked well for most of the datasets, but it worked best for datasets with Directed graphs. The results seemed less relevant for undirected graphs because each edge specifies a two way relation between two nodes. Directed graphs are more specific in that a link to a page does not necessarily imply that page links back. For this reason we conclude that pageRank is much more useful on directed graphs. Also, at first we only iterated over the graph once, but realizing that we need to recalibrate the links after every run, we ran it over the graph multiple times, which yielded much better results.