Exercice1.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercice 1: PageRank on Harvard Data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[(array(['MathWorks/Harvard500'], dtype='<U20'), array(['Web matrix (Numerical Computing with MATLAB, Moler, 2004)'],\n",
      "      dtype='<U57'), <500x500 sparse matrix of type '<class 'numpy.float64'>'\n",
      "\twith 2636 stored elements in Compressed Sparse Column format>, array([[1172]], dtype=uint16), array(['directed graph'], dtype='<U14'), array([[(array(['http://www.harvard.edu                                                                       ',\n",
      "       'http://atwork.harvard.edu                                                                    ',\n",
      "       'http://lib.harvard.edu                                                                       ',\n",
      "       'http://www.president.harvard.edu                                                             ',\n",
      "       'http://www.athletics.harvard.edu                                                             ',\n",
      "       'http://www.haa.harvard.edu                                                                   ',\n",
      "       'http://search.harvard.edu:8765                                                               ',\n",
      "       'http://www.fas.harvard.edu                                                                   ',\n",
      "       'http://www.ksg.harvard.edu                                                                   ',\n",
      "       'http://www.hbs.edu                                                                           ',\n",
      "       'http://www.law.harvard.edu                                                                   ',\n",
      "       'http://www.dce.harvard.edu                                                                   ',\n",
      "       'http://www.hsdm.med.harvard.edu                                                              ',\n",
      "       'http://www.gsd.harvard.edu                                                                   ',\n",
      "       'http://www.hms.harvard.edu                                                                   ',\n",
      "       'http://www.hds.harvard.edu                                                                   ',\n",
      "       'http://www.hsph.harvard.edu                                                                  ',\n",
      "       'http://www.gse.harvard.edu                                                                   ',\n",
      "       'http://www.radcliffe.edu                                                                     ',\n",
      "       'http://www.news.harvard.edu/gazette/daily/0302/03-shuttle.html                               ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.30/17-caspian.html                               ',\n",
      "       'http://www.news.harvard.edu/gazette/daily/0302/03-berman.html                                ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.30/13-naturalgas.html                            ',\n",
      "       'http://www.dfci.harvard.edu/abo/news/press/013003.asp                                        ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.30/01-mercury.html                               ',\n",
      "       'http://www.news.harvard.edu/gazette/calendar                                                 ',\n",
      "       'http://www.researchmatters.harvard.edu                                                       ',\n",
      "       'http://www.universityombuds.harvard.edu                                                      ',\n",
      "       'http://www.president.harvard.edu/speeches/2003/mlk.html                                      ',\n",
      "       'http://atwork.harvard.edu/hrproj-hotline.html                                                ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:hollisct                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:viaxxxxx                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:oasisxxx                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:hgeodesy                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:harvmitd                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:bakercat                                          ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:dumboaks                                          ',\n",
      "       'http://195.31.145.6:4505/ALEPH                                                               ',\n",
      "       'http://hul.harvard.edu/calendar                                                              ',\n",
      "       'http://hul.harvard.edu                                                                       ',\n",
      "       'http://lib.harvard.edu/e-resources/details/f/factivac.html                                   ',\n",
      "       'http://search.harvard.edu:8765/custom/query.html                                             ',\n",
      "       'http://presidenttest.harvard.edu/search                                                      ',\n",
      "       'http://www.provost.harvard.edu                                                               ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.16/01-financialaid.html                          ',\n",
      "       'http://www.gocrimson.com                                                                     ',\n",
      "       'http://sid.harvard.edu:8765/query.html                                                       ',\n",
      "       'http://www.google.com/u/harvarduis                                                           ',\n",
      "       'http://www.google.com                                                                        ',\n",
      "       'http://www.fas.harvard.edu/cgi-bin/phones                                                    ',\n",
      "       'http://www.uis.harvard.edu/telecom                                                           ',\n",
      "       'http://whitepages.med.harvard.edu                                                            ',\n",
      "       'http://www.harvard.edu/listing                                                               ',\n",
      "       'http://www.harvard.edu/academics/academicdepts.html                                          ',\n",
      "       'http://www.harvard.edu/academics/research.html                                               ',\n",
      "       'http://www.harvard.edu/administration/adminlist.html                                         ',\n",
      "       'http://www.hcs.harvard.edu/directory/index.shtml                                             ',\n",
      "       'http://www.harvard.edu/help/noframes/faq12_nf.html                                           ',\n",
      "       'http://www.uis.harvard.edu/telecom/directory/bldgs/bldg.html                                 ',\n",
      "       'http://www.fas.harvard.edu/home/menu.js                                                      ',\n",
      "       'http://www.college.harvard.edu                                                               ',\n",
      "       'http://www.gsas.harvard.edu                                                                  ',\n",
      "       'http://www.deas.harvard.edu                                                                  ',\n",
      "       'http://www.fas.harvard.edu/home/news_and_events/topstory.html                                ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.30/03-cohen.html                                 ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.30/04-hasty.html                                 ',\n",
      "       'http://www.ksg.harvard.edu/news/ksg_in_the_news_013103.htm                                   ',\n",
      "       'http://www.ksg.harvard.edu/news/ethiopia_project_013002.htm                                  ',\n",
      "       'http://www.ksg.harvard.edu/news/opeds/walt_saddam_box_nyt_020203.htm                         ',\n",
      "       'http://www.ksg.harvard.edu/news/experts/kayyem_shoe_bomber_013103.htm                        ',\n",
      "       'http://www.ksg.harvard.edu/news/opeds/euchner_overhaul_state_020203.htm                      ',\n",
      "       'http://www.ksg.harvard.edu/news/korea_forum_013002.htm                                       ',\n",
      "       'http://www.ksg.harvard.edu/news/experts/glickman_state_of_the_union_012903.htm               ',\n",
      "       'http://www.ksg.harvard.edu/press/iopfellows_spring2003.htm                                   ',\n",
      "       'http://www.ksg.harvard.edu/research/working_papers/index.htm                                 ',\n",
      "       'http://www.ksg.harvard.edu/kennedy.shtml                                                     ',\n",
      "       'http://www.ksg.harvard.edu/apply                                                             ',\n",
      "       'http://ksghome.harvard.edu/~.jnye.dean.ksg/visitingcom                                       ',\n",
      "       'http://www.ksg.harvard.edu/ksgpress/bulletin                                                 ',\n",
      "       'http://www.ksg.harvard.edu/ksgpress/students/directns.htm                                    ',\n",
      "       'http://www.ksg.harvard.edu/news/announcements                                                ',\n",
      "       'http://www.ksg.harvard.edu/giving                                                            ',\n",
      "       'http://ksgnotes1.harvard.edu/outdisc/Emergenc.nsf/Announcements                              ',\n",
      "       'http://ksgnotes1.harvard.edu/intranet                                                        ',\n",
      "       'http://www.harvard.edu/copyright.html                                                        ',\n",
      "       'http://www.ksg.harvard.edu/ksgtoday                                                          ',\n",
      "       'http://www.ksg.harvard.edu/iop                                                               ',\n",
      "       'http://ksgnotes1.harvard.edu/faculty                                                         ',\n",
      "       'http://www.execprog.com/home.asp                                                             ',\n",
      "       'http://www.ksg.harvard.edu/TS/coursepage.htm                                                 ',\n",
      "       'http://www.ksgcase.harvard.edu                                                               ',\n",
      "       'http://www.ifactory.com                                                                      ',\n",
      "       'http://www.cglv.hbs.edu                                                                      ',\n",
      "       'http://www.hbsi.hbs.edu/custom/index.htm                                                     ',\n",
      "       'http://www.hbs.edu/career_services                                                           ',\n",
      "       'http://www.hbs.edu/research                                                                  ',\n",
      "       'http://hbswk.hbs.edu                                                                         ',\n",
      "       'http://www.hbs.edu/mba/index.html                                                            ',\n",
      "       'http://www.alumni.hbs.edu/index.html                                                         ',\n",
      "       'http://www.exed.hbs.edu/index.html                                                           ',\n",
      "       'http://www.hbs.edu:8765                                                                      ',\n",
      "       'http://www.hbs.edu/siteindex/siteindex.html                                                  ',\n",
      "       'http://www.hbs.edu/about/contact.html                                                        ',\n",
      "       'http://www.hbs.edu/about                                                                     ',\n",
      "       'http://www.hbs.edu/it                                                                        ',\n",
      "       'http://www.library.hbs.edu                                                                   ',\n",
      "       'http://harvardbusinessonline.hbsp.harvard.edu                                                ',\n",
      "       'http://www.hbs.edu/hr                                                                        ',\n",
      "       'http://www.harvard.edu/siteguide/copyright.html                                              ',\n",
      "       'http://internal.law.harvard.edu/adviser                                                      ',\n",
      "       'http://www.law.harvard.edu/events                                                            ',\n",
      "       'http://www.law.harvard.edu/Administrative_Services/Registrar/Bulletin/academic_calendar.shtml',\n",
      "       'http://internal.law.harvard.edu/adviser/submit.html                                          ',\n",
      "       'http://i-cuisines.com/SodexhoCafe/Harkness                                                   ',\n",
      "       'http://www.dce.harvard.edu/extension                                                         ',\n",
      "       'http://www.dce.harvard.edu/summer                                                            ',\n",
      "       'http://www.dce.harvard.edu/ssp                                                               ',\n",
      "       'http://www.dce.harvard.edu/iel                                                               ',\n",
      "       'http://www.dce.harvard.edu/hilr                                                              ',\n",
      "       'http://www.dce.harvard.edu/pubs                                                              ',\n",
      "       'http://www.hsdm.harvard.edu                                                                  ',\n",
      "       'http://www.cabengo.com                                                                       ',\n",
      "       'http://www.hmcnet.harvard.edu                                                                ',\n",
      "       'http://www.med.harvard.edu/alumni.html                                                       ',\n",
      "       'http://www.med.harvard.edu/publications/pubs.html                                            ',\n",
      "       'http://medapps.med.harvard.edu/eventscal/asp-html/index.asp                                  ',\n",
      "       'http://www.hms.harvard.edu/hr                                                                ',\n",
      "       'http://www.hms.harvard.edu/student                                                           ',\n",
      "       'http://www.countway.med.harvard.edu                                                          ',\n",
      "       'http://www.med.harvard.edu                                                                   ',\n",
      "       'http://webweekly.hms.harvard.edu                                                             ',\n",
      "       'http://www.intelihealth.com                                                                  ',\n",
      "       'http://www.hms.harvard.edu/education.html                                                    ',\n",
      "       'http://www.hms.harvard.edu/md/index.html                                                     ',\n",
      "       'http://www.hms.harvard.edu/dms/phdprograms.html                                              ',\n",
      "       'http://www.hms.harvard.edu/md_phd/index.html                                                 ',\n",
      "       'http://www.hms.harvard.edu/dualdegrees/index.html                                            ',\n",
      "       'http://www.hms.harvard.edu/research.html                                                     ',\n",
      "       'http://sbweb.med.harvard.edu/~bcmp                                                           ',\n",
      "       'http://cbweb.med.harvard.edu/default.html                                                    ',\n",
      "       'http://genetics.med.harvard.edu                                                              ',\n",
      "       'http://www.hms.harvard.edu/dms/bbs/micro                                                     ',\n",
      "       'http://neuro.med.harvard.edu                                                                 ',\n",
      "       'http://www.hmcnet.harvard.edu/pathol                                                         ',\n",
      "       'http://www.hms.harvard.edu/ambulatory/dacp.html                                              ',\n",
      "       'http://www.hcp.med.harvard.edu                                                               ',\n",
      "       'http://www.hms.harvard.edu/dsm                                                               ',\n",
      "       'http://www.hmcnet.harvard.edu/clinical/index.html                                            ',\n",
      "       'http://www.hms.harvard.edu/cdi                                                               ',\n",
      "       'http://www.hms.harvard.edu/administration.html                                               ',\n",
      "       'http://www.hms.harvard.edu/diversity                                                         ',\n",
      "       'http://www.hms.harvard.edu/fa                                                                ',\n",
      "       'http://www.hms.harvard.edu/it                                                                ',\n",
      "       'http://www.bidmc.harvard.edu                                                                 ',\n",
      "       'http://www.partners.org/bwh                                                                  ',\n",
      "       'http://www.va.gov/525brockton                                                                ',\n",
      "       'http://www.challiance.org                                                                    ',\n",
      "       'http://sprsgi.med.harvard.edu                                                                ',\n",
      "       'http://www.childrenshospital.org                                                             ',\n",
      "       'http://www.dfci.harvard.edu                                                                  ',\n",
      "       'http://www.harvardpilgrim.org                                                                ',\n",
      "       'http://www.joslin.org                                                                        ',\n",
      "       'http://www.meei.harvard.edu                                                                  ',\n",
      "       'http://www.mgh.harvard.edu                                                                   ',\n",
      "       'http://www.mcleanhospital.org                                                                ',\n",
      "       'http://www.mtauburn.caregroup.org                                                            ',\n",
      "       'http://www.eri.harvard.edu                                                                   ',\n",
      "       'http://spauldingrehab.org                                                                    ',\n",
      "       'http://www.hds.harvard.edu/about.html                                                        ',\n",
      "       'http://www.hds.harvard.edu/afa                                                               ',\n",
      "       'http://www.hds.harvard.edu/facstaff.html                                                     ',\n",
      "       'http://www.hds.harvard.edu/students.html                                                     ',\n",
      "       'http://www.hds.harvard.edu/library                                                           ',\n",
      "       'http://www.hds.harvard.edu/administration.html                                               ',\n",
      "       'http://www.hds.harvard.edu/cswr                                                              ',\n",
      "       'http://www.hds.harvard.edu/centers.html                                                      ',\n",
      "       'http://www.hds.harvard.edu/dpa                                                               ',\n",
      "       'http://www.hds.harvard.edu/publications.html                                                 ',\n",
      "       'http://www.hds.harvard.edu/dpa/alums                                                         ',\n",
      "       'http://www.hds.harvard.edu/dpa/news/calendar.html                                            ',\n",
      "       'http://www.whomentoredyou.org                                                                ',\n",
      "       'http://www.yourcancerrisk.harvard.edu                                                        ',\n",
      "       'http://www.worldhealthnews.harvard.edu                                                       ',\n",
      "       'http://www.washingtonpost.com/wp-dyn/articles/A30481-2003Jan8.html                           ',\n",
      "       'http://www.gse.harvard.edu/admissions                                                        ',\n",
      "       'http://www.gse.harvard.edu/financialaid                                                      ',\n",
      "       'http://www.gse.harvard.edu/academics.html                                                    ',\n",
      "       'http://www.gse.harvard.edu/welcome                                                           ',\n",
      "       'http://www.gse.harvard.edu/~catalog                                                          ',\n",
      "       'http://hugse9.harvard.edu/gsedata/calendar_pkg.academic_calendar                             ',\n",
      "       'http://www.gse.harvard.edu/~oasweb                                                           ',\n",
      "       'http://www.gse.harvard.edu/library                                                           ',\n",
      "       'http://www.gse.harvard.edu/library/*RS/research-services.html                                ',\n",
      "       'http://holliscatalog.harvard.edu                                                             ',\n",
      "       'http://gseweb.harvard.edu/~conf                                                              ',\n",
      "       'http://gseweb.harvard.edu/~osa                                                               ',\n",
      "       'http://gseweb.harvard.edu/~ltc                                                               ',\n",
      "       'http://gseweb.harvard.edu/students.html#careerresources                                      ',\n",
      "       'http://gseweb.harvard.edu/students.html                                                      ',\n",
      "       'http://www.gse.harvard.edu/faculty_profiles.html                                             ',\n",
      "       'http://www.gse.harvard.edu/research.html                                                     ',\n",
      "       'http://www.gse.harvard.edu/~ltc                                                              ',\n",
      "       'http://www.gse.harvard.edu/faculty.html                                                      ',\n",
      "       'http://gseweb.harvard.edu/~oasweb/positions.html                                             ',\n",
      "       'http://gseweb.harvard.edu/news                                                               ',\n",
      "       'http://hugse9.harvard.edu/gsedata/calendar_pkg.display_calendar                              ',\n",
      "       'http://www.gse.harvard.edu/~hepg                                                             ',\n",
      "       'http://www.gse.harvard.edu/facstaff.html                                                     ',\n",
      "       'http://www.gse.harvard.edu/pubs.html                                                         ',\n",
      "       'http://www.gse.harvard.edu/alumni                                                            ',\n",
      "       'http://www.gse.harvard.edu/alumni/classnotes                                                 ',\n",
      "       'http://www.gse.harvard.edu/alumni/services                                                   ',\n",
      "       'http://www.gse.harvard.edu/prodev.html                                                       ',\n",
      "       'http://www.gse.harvard.edu/news                                                              ',\n",
      "       'http://www.gse.harvard.edu/news/features/merseth02012003.html                                ',\n",
      "       'http://www.civilrightsproject.harvard.edu/news/pressreleases.php/record_id=27                ',\n",
      "       'http://www.onpointradio.org/shows/2003/01/20030120_b_main.asp                                ',\n",
      "       'http://www.news.harvard.edu/gazette/daily/0301/15-finaid.html                                ',\n",
      "       'http://www.gse.harvard.edu/use.html                                                          ',\n",
      "       'http://www.gse.harvard.edu/administrative.html                                               ',\n",
      "       'http://gseweb.harvard.edu/search                                                             ',\n",
      "       'http://www.gse.harvard.edu/sitemap.html                                                      ',\n",
      "       'http://www.gse.harvard.edu/search.html                                                       ',\n",
      "       'http://hugse9.harvard.edu/gsedata/calendar_pkg.forums#2062                                   ',\n",
      "       'http://gseweb.harvard.edu/aie                                                                ',\n",
      "       'http://www.gse.harvard.edu/~src_web                                                          ',\n",
      "       'http://www.gse.harvard.edu/~aocc                                                             ',\n",
      "       'http://www.gse.harvard.edu/~admit/directions.html                                            ',\n",
      "       'http://www.radcliffe.edu/administration/index.html                                           ',\n",
      "       'http://www.radcliffe.edu/contacts/index.html                                                 ',\n",
      "       'http://www.radcliffe.edu/students/index.html                                                 ',\n",
      "       'http://www.radcliffe.edu/dev/index.html                                                      ',\n",
      "       'http://www.radcliffe.edu/news/index.html                                                     ',\n",
      "       'http://www.radcliffe.edu/alumnae/index.html                                                  ',\n",
      "       'http://www.radcliffe.edu/search/SearchRad.html                                               ',\n",
      "       'http://www.radcliffe.edu/about/index.html                                                    ',\n",
      "       'http://www.radcliffe.edu/research/index.html                                                 ',\n",
      "       'http://www.radcliffe.edu/fellowships/index.html                                              ',\n",
      "       'http://www.radcliffe.edu/schles/index.html                                                   ',\n",
      "       'http://www.radcliffe.edu/events/index.html                                                   ',\n",
      "       'http://www.radcliffe.edu/murray/index.html                                                   ',\n",
      "       'http://www.enterprisingwomenexhibit.org                                                      ',\n",
      "       'http://www.radcliffe.edu/vpi                                                                 ',\n",
      "       'http://www.radcliffe.edu/murray/evntnews/brbgsp03.htm                                        ',\n",
      "       'http://www.radcliffe.edu/news/pr/030128_david.html                                           ',\n",
      "       'http://www.radcliffe.edu/quarterly/200301                                                    ',\n",
      "       'http://www.radcliffe.edu/events/lectures/2003_dean.html#guth                                 ',\n",
      "       'http://www.radcliffe.edu/fellowships/events/index.html#rocheleau                             ',\n",
      "       'http://www.news.harvard.edu/gazette/search                                                   ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/news.html                                     ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/science.html                                  ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/profiles.html                                 ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/community.html                                ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/sports.html                                   ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/campus.html                                   ',\n",
      "       'http://www.news.harvard.edu/gazette/2003/01.09/arts.html                                     ',\n",
      "       'http://www.president.harvard.edu/speeches/2003/columbia.html                                 ',\n",
      "       'http://www.news.harvard.edu/guide                                                            ',\n",
      "       'http://www.news.harvard.edu/tour                                                             ',\n",
      "       'http://search.harvard.edu:8765/query.html                                                    ',\n",
      "       'http://www.dana-farber.org/favicon.ico                                                       ',\n",
      "       'http://www.dana-farber.org                                                                   ',\n",
      "       'http://www.dana-farber.org/abo                                                               ',\n",
      "       'http://www.dana-farber.org/abo/news                                                          ',\n",
      "       'http://www.dana-farber.org/abo/news/press                                                    ',\n",
      "       'http://www.dana-farber.org/abo/mission                                                       ',\n",
      "       'http://www.dana-farber.org/abo/history                                                       ',\n",
      "       'http://www.dana-farber.org/abo/news/pressarchive                                             ',\n",
      "       'http://www.dana-farber.org/abo/news/facts                                                    ',\n",
      "       'http://www.dana-farber.org/abo/news/publications                                             ',\n",
      "       'http://www.dana-farber.org/abo/news/links                                                    ',\n",
      "       'http://www.dana-farber.org/abo/news/for                                                      ',\n",
      "       'http://www.dana-farber.org/abo/news/broadcasts                                               ',\n",
      "       'http://www.dana-farber.org/abo/danafarber                                                    ',\n",
      "       'http://www.dana-farber.org/abo/medical                                                       ',\n",
      "       'http://www.dana-farber.org/abo/community                                                     ',\n",
      "       'http://www.dana-farber.org/abo/affiliations                                                  ',\n",
      "       'http://www.dana-farber.org/abo/departmentindex                                               ',\n",
      "       'http://www.dana-farber.org/abo/working                                                       ',\n",
      "       'http://www.dana-farber.org/abo/award                                                         ',\n",
      "       'http://www.jimmyfund.org                                                                     ',\n",
      "       'http://www.researchmatters.harvard.edu/search                                                ',\n",
      "       'http://www.workingatharvard.org                                                              ',\n",
      "       'http://www.radcliffe.edu/schles                                                              ',\n",
      "       'http://www.library.hbs.edu/hc                                                                ',\n",
      "       'http://www.law.harvard.edu/library/special/index.htm                                         ',\n",
      "       'http://hcl.harvard.edu/finearts/sdi.html                                                     ',\n",
      "       'http://hul.harvard.edu/huarc                                                                 ',\n",
      "       'http://www.artmuseums.harvard.edu                                                            ',\n",
      "       'http://hcl.harvard.edu/harvard-yenching                                                      ',\n",
      "       'http://www.gsd.harvard.edu/library/visres/visres.htm                                         ',\n",
      "       'http://www.peabody.harvard.edu                                                               ',\n",
      "       'http://hollisweb.harvard.edu                                                                 ',\n",
      "       'http://hul.harvard.edu/ois/systems/oasis                                                     ',\n",
      "       'http://hgl.harvard.edu/keywordhelp.html                                                      ',\n",
      "       'http://hgl.harvard.edu/titlehelp.html                                                        ',\n",
      "       'http://hgl.harvard.edu/authorhelp.html                                                       ',\n",
      "       'http://www.macromedia.com/go/getflashplayer                                                  ',\n",
      "       'http://vdc-prod.hmdc.harvard.edu/VDC/index.jsp                                               ',\n",
      "       'http://hbsworkingknowledge.hbs.edu                                                           ',\n",
      "       'http://www.library.hbs.edu/genref/libraries.htm                                              ',\n",
      "       'http://www.ils.doaks.org                                                                     ',\n",
      "       'http://hul.harvard.edu/objects/topnav.js                                                     ',\n",
      "       'http://hul.harvard.edu/objects/links.js                                                      ',\n",
      "       'http://hcl.harvard.edu/news/stories/shoes.html                                               ',\n",
      "       'http://www.ala.org/events/annual2003                                                         ',\n",
      "       'http://hul.harvard.edu/objects/copyright.js                                                  ',\n",
      "       'http://hul.harvard.edu/objects/address.js                                                    ',\n",
      "       'http://nrs.harvard.edu/urn-3:hul.eresource:factivac                                          ',\n",
      "       'http://www.cid.harvard.edu/events/africa_sem.html                                            ',\n",
      "       'http://www.provost.harvard.edu/it_fund                                                       ',\n",
      "       'http://www.fas.harvard.edu/~asiactr                                                          ',\n",
      "       'http://www.international.harvard.edu                                                         ',\n",
      "       'http://www.gse.harvard.edu/~hci                                                              ',\n",
      "       'http://www.fas.harvard.edu/~athletic/tickets                                                 ',\n",
      "       'http://www.gocrimson.com/ot/eclubnews.html                                                   ',\n",
      "       'http://gocrimson.ocsn.com                                                                    ',\n",
      "       'http://gocrimson.ocsn.com/ot/broadcastinfo.html                                              ',\n",
      "       'http://gocrimson.ocsn.com/compliance/harv-compliance.html                                    ',\n",
      "       'http://gocrimson.ocsn.com/directions/harv-directions.html                                    ',\n",
      "       'http://gocrimson.ocsn.com/facilities/rec_facilities.html                                     ',\n",
      "       'http://gocrimson.ocsn.com/trads/harv-trads.html                                              ',\n",
      "       'http://gocrimson.ocsn.com/links/harv-links.html                                              ',\n",
      "       'http://gocrimson.ocsn.com/ot/harv-recreation.html                                            ',\n",
      "       'http://gocrimson.ocsn.com/recruiting/harv-recruiting.html                                    ',\n",
      "       'http://www.fas.harvard.edu/~athletic/schedule_winter.html                                    ',\n",
      "       'http://gocrimson.ocsn.com/site-map/harv-site-map.html                                        ',\n",
      "       'http://gocrimson.ocsn.com/staffdir/harv-staffdir.html                                        ',\n",
      "       'http://gocrimson.ocsn.com/tickets/harv-tickets.html                                          ',\n",
      "       'http://www.varsityclub.harvard.edu                                                           ',\n",
      "       'http://www.ocsn.com                                                                          ',\n",
      "       'http://gocrimson.ocsn.com/sports/m-baskbl/sched/harv-m-baskbl-sched.html                     ',\n",
      "       'http://gocrimson.ocsn.com/ot/sesquicentennial.html                                           ',\n",
      "       'http://www.ocsn.com/cgi-bin/census/census.cgi                                                ',\n",
      "       'http://www.studentadvantage.com                                                              ',\n",
      "       'http://www.uis.harvard.edu/technology_services/specials/applelogin.php                       ',\n",
      "       'http://www.cait.harvard.edu/PC_letter1.doc                                                   ',\n",
      "       'http://www.dining.harvard.edu/frameset_cat.html                                              ',\n",
      "       'http://www.uis.harvard.edu/server_hosting/hosting_monitoring.php                             ',\n",
      "       'http://www.hfc.harvard.edu/functions                                                         ',\n",
      "       'http://www.cait.harvard.edu                                                                  ',\n",
      "       'http://www.harvard.edu/infotech                                                              ',\n",
      "       'http://www.cait.harvard.edu/training/competencies.php                                        ',\n",
      "       'http://fas-www.harvard.edu/fas/directory.shtml                                               ',\n",
      "       'http://www.abcd.harvard.edu                                                                  ',\n",
      "       'http://able.harvard.edu                                                                      ',\n",
      "       'http://www.laspau.harvard.edu                                                                ',\n",
      "       'http://www.hbs.edu/units/ac                                                                  ',\n",
      "       'http://learnweb.harvard.edu/alps                                                             ',\n",
      "       'http://adams.student.harvard.edu                                                             ',\n",
      "       'http://www.adapt.harvard.edu                                                                 ',\n",
      "       'http://www.fas.harvard.edu/~ims                                                              ',\n",
      "       'http://www.hms.harvard.edu/doa                                                               ',\n",
      "       'http://www.gse.harvard.edu/~apsp                                                             ',\n",
      "       'http://www.fas.harvard.edu/~fasadapt                                                         ',\n",
      "       'http://www.gse.harvard.edu/~admin                                                            ',\n",
      "       'http://www.hbs.edu/mba/admissions.html                                                       ',\n",
      "       'http://www.hsdm.med.harvard.edu/pages/edu.htm                                                ',\n",
      "       'http://www.gsd.harvard.edu/admissions                                                        ',\n",
      "       'http://www.gsas.harvard.edu/admissions                                                       ',\n",
      "       'http://www.gse.harvard.edu/~admit                                                            ',\n",
      "       'http://www.law.harvard.edu/Admissions                                                        ',\n",
      "       'http://www.hms.harvard.edu/admissions                                                        ',\n",
      "       'http://www.hsph.harvard.edu/admissions.html                                                  ',\n",
      "       'http://adm-is.fas.harvard.edu                                                                ',\n",
      "       'http://www.gse.harvard.edu/~ncsall                                                           ',\n",
      "       'http://www.gsd.harvard.edu/academic/asp                                                      ',\n",
      "       'http://www.amrep.org/iatt                                                                    ',\n",
      "       'http://www.oap.harvard.edu/DivDir/diversity.html                                             ',\n",
      "       'http://www.fas.harvard.edu/~afroam                                                           ',\n",
      "       'http://www.fas.harvard.edu/~cafrica                                                          ',\n",
      "       'http://www.fas.harvard.edu/~ofa/programs/theater/schedule.html                               ',\n",
      "       'http://www.hms.harvard.edu/aging                                                             ',\n",
      "       'http://www.aids.harvard.edu                                                                  ',\n",
      "       'http://www.aids.harvard.edu/publications/har/index.html                                      ',\n",
      "       'http://www.fas.harvard.edu/~iaas                                                             ',\n",
      "       'http://www.gsas.harvard.edu/alumni                                                           ',\n",
      "       'http://www.gsd.harvard.edu/inside/dev_alumni                                                 ',\n",
      "       'http://www.alumni.hbs.edu                                                                    ',\n",
      "       'http://www.hsdm.med.harvard.edu/pages/alumni/alumni.html                                     ',\n",
      "       'http://www.law.harvard.edu/alumni                                                            ',\n",
      "       'http://www.hms.harvard.edu/alumni                                                            ',\n",
      "       'http://www.ksg.harvard.edu/alum                                                              ',\n",
      "       'http://www.hsph.harvard.edu/alumni                                                           ',\n",
      "       'http://www.hms.harvard.edu/ambulatory/index.html                                             ',\n",
      "       'http://www.fas.harvard.edu/~amciv                                                            ',\n",
      "       'http://www.fas.harvard.edu/~cwc                                                              ',\n",
      "       'http://www.ksg.harvard.edu/hpaied                                                            ',\n",
      "       'http://www.fas.harvard.edu/english                                                           ',\n",
      "       'http://caps.gov.harvard.edu                                                                  ',\n",
      "       'http://www.amrep.org                                                                         ',\n",
      "       'http://www.law.harvard.edu/programs/ames_foundation/main.html                                ',\n",
      "       'http://www.kinetics.harvard.edu                                                              ',\n",
      "       'http://www.arp.harvard.edu                                                                   ',\n",
      "       'http://www.hmcnet.harvard.edu/anesthesia                                                     ',\n",
      "       'http://www.law.harvard.edu/programs/annual_review                                            ',\n",
      "       'http://www.wjh.harvard.edu/anthro                                                            ',\n",
      "       'http://www.deas.harvard.edu/graduate                                                         ',\n",
      "       'http://www.huaquatics.harvard.edu                                                            ',\n",
      "       'http://billie.harvard.edu                                                                    ',\n",
      "       'http://www.arboretum.harvard.edu                                                             ',\n",
      "       'http://www.gsd.harvard.edu/academic/arch                                                     ',\n",
      "       'http://www.gsd.harvard.edu/academic/la                                                       ',\n",
      "       'http://www.huh.harvard.edu/libraries/arnold.htm                                              ',\n",
      "       'http://www.arts-civic.org                                                                    ',\n",
      "       'http://wodewick.fas.harvard.edu                                                              ',\n",
      "       'http://www.fas.harvard.edu/~ofa                                                              ',\n",
      "       'http://www.gse.harvard.edu/~aie_web                                                          ',\n",
      "       'http://www.ap.harvard.edu                                                                    ',\n",
      "       'http://www.ksg.harvard.edu/cbg/asia                                                          ',\n",
      "       'http://www.gse.harvard.edu/forums                                                            ',\n",
      "       'http://www.oap.harvard.edu                                                                   ',\n",
      "       'http://cfa-www.harvard.edu/hco/astron.html                                                   ',\n",
      "       'http://cfa-www.harvard.edu                                                                   ',\n",
      "       'http://cfa-www.harvard.edu/library                                                           ',\n",
      "       'http://cfa-www.harvard.edu/cfa/tad                                                           ',\n",
      "       'http://www.fas.harvard.edu/~athletic                                                         ',\n",
      "       'http://www.fas.harvard.edu/~atlantic                                                         ',\n",
      "       'http://www.as.harvard.edu                                                                    ',\n",
      "       'http://www.fas.harvard.edu/academics/departments/all.html                                    ',\n",
      "       'http://www.hbs.edu/fac                                                                       ',\n",
      "       'http://www.gsd.harvard.edu/academic                                                          ',\n",
      "       'http://www.hds.harvard.edu/apc.html                                                          ',\n",
      "       'http://www.ksg.harvard.edu/programs                                                          ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups                                          ',\n",
      "       'http://www.hms.harvard.edu/bss                                                               ',\n",
      "       'http://www.hsph.harvard.edu/about.html#departments                                           ',\n",
      "       'http://www.gsd.harvard.edu/depts/asp                                                         ',\n",
      "       'http://web-dubois.fas.harvard.edu                                                            ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/antitrust.php                            ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/applied_math/index.html                            ',\n",
      "       'http://www.gsd.harvard.edu/depts/archdept                                                    ',\n",
      "       'http://www-hugsas.harvard.edu/webfiles/admis/socsci/archtect.htm                             ',\n",
      "       'http://bcmp.med.harvard.edu                                                                  ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/bsdm.html                          ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/bsph.html                          ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/engineering_sciences/biomedical.html               ',\n",
      "       'http://twod.med.harvard.edu/labgc/biophysics                                                 ',\n",
      "       'http://www.biostat.harvard.edu                                                               ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/busecon.html                       ',\n",
      "       'http://www.hbs.edu/units/bgie                                                                ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/special.html                       ',\n",
      "       'http://www.hsph.harvard.edu/Academics/ccb/index.html                                         ',\n",
      "       'http://cellbio.med.harvard.edu                                                               ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/chemphys.html                      ',\n",
      "       'http://www.chem.harvard.edu                                                                  ',\n",
      "       'http://www.fas.harvard.edu/~classics                                                         ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/commercial.php                           ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/complit.html                       ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/computer_science/index.html                        ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/constitution.php                         ',\n",
      "       'http://icg.harvard.edu/~core                                                                 ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/corporate.php                            ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/criminal.php                             ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/cyberlaw.php                             ',\n",
      "       'http://www.hms.harvard.edu/dms                                                               ',\n",
      "       'http://www.eps.harvard.edu                                                                   ',\n",
      "       'http://www.fas.harvard.edu/~ealc                                                             ',\n",
      "       'http://www.fas.harvard.edu/~eas                                                              ',\n",
      "       'http://www.economics.harvard.edu                                                             ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/engineering_sciences/electrical.html               ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/employment.php                           ',\n",
      "       'http://www.hsdm.med.harvard.edu/pages/depts/restor/endo/endo.htm                             ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/engineering_sciences/index.html                    ',\n",
      "       'http://www.hbs.edu/units/em                                                                  ',\n",
      "       'http://environment.harvard.edu                                                               ',\n",
      "       'http://www.hsph.harvard.edu/Academics/eh/index.html                                          ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/environment.php                          ',\n",
      "       'http://environment.harvard.edu/espp                                                          ',\n",
      "       'http://www.deas.harvard.edu/undergraduate/engineering_sciences/environmental.html            ',\n",
      "       'http://www.hsph.harvard.edu/Academics/epidem                                                 ',\n",
      "       'http://www.fas.harvard.edu/~cesh                                                             ',\n",
      "       'http://www.gse.harvard.edu/~admit/progs-edm-mi-etp.html                                      ',\n",
      "       'http://www.fas.harvard.edu/~expos                                                            ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/family.php                               ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/federal.php                              ',\n",
      "       'http://www.gse.harvard.edu/~fep                                                              ',\n",
      "       'http://www.hbs.edu/units/finance                                                             ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/financial.php                            ',\n",
      "       'http://www.fas.harvard.edu/~folkmyth                                                         ',\n",
      "       'http://www.gsas.harvard.edu/academic/departments/programs/forestry.html                      ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/gender.php                               ',\n",
      "       'http://www.gse.harvard.edu/~genderstudies                                                    ',\n",
      "       'http://www.hbs.edu/units/gm                                                                  ',\n",
      "       'http://www.fas.harvard.edu/~german                                                           ',\n",
      "       'http://www.gov.harvard.edu                                                                   ',\n",
      "       'http://www.gse.harvard.edu/~nap                                                              ',\n",
      "       'http://www.hsph.harvard.edu/Academics/hsb/index.html                                         ',\n",
      "       'http://www.law.harvard.edu/students/catalog/cgroups/health.php                               ',\n",
      "       'http://www.hsph.harvard.edu/Academics/hpm/index.html                                         ',\n",
      "       'http://www.fas.harvard.edu/~healthpl                                                         ',\n",
      "       'http://www.gse.harvard.edu/~highered                                                         ',\n",
      "       'http://www.fas.harvard.edu/~heal/HEAL.html                                                   ',\n",
      "       'http://www.fas.harvard.edu/~histlit                                                          ',\n",
      "       'http://www.fas.harvard.edu/~history                                                          ',\n",
      "       'http://www.fas.harvard.edu/~hoart                                                            ',\n",
      "       'http://www.fas.harvard.edu/~hsdept                                                           ',\n",
      "       'http://www.gse.harvard.edu/~hdp                                                              ',\n",
      "       'http://www.hsph.harvard.edu/Academics/iid/index.html                                         ',\n",
      "       'http://www.hsdm.med.harvard.edu/pages/depts/restor/implant/implant.htm                       '],\n",
      "      dtype='<U93'),)]], dtype=[('nodename', 'O')]), array(['2002'], dtype='<U4'), array(['C. Moler'], dtype='<U8'), array(['T. Davis'], dtype='<U8'))]]\n"
     ]
    }
   ],
   "source": [
    "import scipy.io\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.sparse as sps\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "#Import data\n",
    "mat=scipy.io.loadmat(\"C:/Users/victo/Downloads/Exercise_1/Harvard500.mat\")\n",
    "#print(mat)\n",
    "Pb=mat['Problem']\n",
    "nodename=mat['Problem']['aux'][0,0][0,0][0]\n",
    "print(Pb)\n",
    "#print(type(mat))\n",
    "#print(type(Pb))\n",
    "#pint(Pb.shape)\n",
    "#print(Pb['A'][0,0])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The adjacency matrix of this graph is A_ij=1 if j->i\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "A=Pb['A'][0,0]\n",
    "A=A.toarray()\n",
    "#print(len(A),len(A[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the sparsity structure of the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.spy(sps.csr_matrix(A),markersize=1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create Matrix + first test on pg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: \n",
      "Type: Graph\n",
      "Number of nodes: 500\n",
      "Number of edges: 2116\n",
      "Average degree:   8.4640\n"
     ]
    }
   ],
   "source": [
    "PdA=pd.DataFrame(A)\n",
    "G=nx.from_pandas_adjacency(PdA)\n",
    "print(nx.info(G))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: \n",
      "Type: DiGraph\n",
      "Number of nodes: 500\n",
      "Number of edges: 4159\n",
      "Average in degree:   8.3180\n",
      "Average out degree:   8.3180\n",
      "http://www.harvard.edu                                                                        0.05376144768407083\n",
      "http://atwork.harvard.edu                                                                     0.003200321496738972\n",
      "http://lib.harvard.edu                                                                        0.010345578027386265\n",
      "http://www.president.harvard.edu                                                              0.003574542042529624\n",
      "http://www.athletics.harvard.edu                                                              0.0027141954178884404\n",
      "http://www.haa.harvard.edu                                                                    0.0035368516011862654\n",
      "http://search.harvard.edu:8765                                                                0.006310217638113741\n",
      "http://www.fas.harvard.edu                                                                    0.004181341897438184\n",
      "http://www.ksg.harvard.edu                                                                    0.008683643464945198\n",
      "http://www.hbs.edu                                                                            0.007851935906840798\n",
      "http://www.law.harvard.edu                                                                    0.0050509921527790175\n",
      "http://www.dce.harvard.edu                                                                    0.0030741763214208705\n",
      "http://www.hsdm.med.harvard.edu                                                               0.003271732380168758\n",
      "http://www.gsd.harvard.edu                                                                    0.001097312215836577\n",
      "http://www.hms.harvard.edu                                                                    0.01772553630024955\n",
      "http://www.hds.harvard.edu                                                                    0.002888372095095155\n",
      "http://www.hsph.harvard.edu                                                                   0.005984082337210578\n",
      "http://www.gse.harvard.edu                                                                    0.012859686129101808\n",
      "http://www.radcliffe.edu                                                                      0.004031864672046435\n",
      "http://www.news.harvard.edu/gazette/daily/0302/03-shuttle.html                                0.003460123512850082\n",
      "http://www.news.harvard.edu/gazette/2003/01.30/17-caspian.html                                0.0016309827051996918\n",
      "http://www.news.harvard.edu/gazette/daily/0302/03-berman.html                                 0.0034734655644066367\n",
      "http://www.news.harvard.edu/gazette/2003/01.30/13-naturalgas.html                             0.0018884076721789023\n",
      "http://www.dfci.harvard.edu/abo/news/press/013003.asp                                         0.002427868391318674\n",
      "http://www.news.harvard.edu/gazette/2003/01.30/01-mercury.html                                0.0016309827051996918\n",
      "http://www.news.harvard.edu/gazette/calendar                                                  0.004395892215435302\n",
      "http://www.researchmatters.harvard.edu                                                        0.004494246630734898\n",
      "http://www.universityombuds.harvard.edu                                                       0.0009775203959662936\n",
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      "http://www.hsph.harvard.edu/Academics/hsb/index.html                                          0.0007052310718178283\n",
      "http://www.law.harvard.edu/students/catalog/cgroups/health.php                                0.0006301952651676138\n",
      "http://www.hsph.harvard.edu/Academics/hpm/index.html                                          0.0007052310718178283\n",
      "http://www.fas.harvard.edu/~healthpl                                                          0.0009017035644239934\n",
      "http://www.gse.harvard.edu/~highered                                                          0.0017518275607478916\n",
      "http://www.fas.harvard.edu/~heal/HEAL.html                                                    0.00038649408257492154\n",
      "http://www.fas.harvard.edu/~histlit                                                           0.00038649408257492154\n",
      "http://www.fas.harvard.edu/~history                                                           0.0006301952651676138\n",
      "http://www.fas.harvard.edu/~hoart                                                             0.0007010766325146554\n",
      "http://www.fas.harvard.edu/~hsdept                                                            0.0006200005722930636\n",
      "http://www.gse.harvard.edu/~hdp                                                               0.0012933774201459994\n",
      "http://www.hsph.harvard.edu/Academics/iid/index.html                                          0.0007052310718178283\n",
      "http://www.hsdm.med.harvard.edu/pages/depts/restor/implant/implant.htm                        0.0010139071244502646\n"
     ]
    }
   ],
   "source": [
    "#Pagerank function of networkx library, permite to test the veracity of the code\n",
    "#Pg=nx.pagerank(G,0.95, tol=1e-4)\n",
    "\n",
    "tol=1e-4\n",
    "alpha=0.95\n",
    "D=nx.to_directed(G)\n",
    "W=nx.stochastic_graph(D)\n",
    "print(nx.info(W))\n",
    "N=W.number_of_nodes()\n",
    "\n",
    "\n",
    "x=dict.fromkeys(W,1.0/N)\n",
    "p=dict.fromkeys(W,1.0/N)\n",
    "\n",
    "dangling_weight=p\n",
    "dangling_nodes = [n for n in W if W.out_degree(n) == 0.0] \n",
    "\n",
    "\n",
    "for _ in range(100): \n",
    "    xlast = x \n",
    "    x = dict.fromkeys(xlast.keys(), 0) \n",
    "    danglesum = alpha * sum(xlast[n] for n in dangling_nodes) \n",
    "    for n in x:\n",
    "        \n",
    "    # this matrix multiply looks odd because it is \n",
    "    # doing a left multiply x^T=xlast^T*W \n",
    "        for nbr in W[n]: \n",
    "            x[nbr] += alpha * xlast[n]*W[n][nbr]['weight']\n",
    "        x[n] += danglesum * dangling_weight[n] + (1.0 - alpha) * p[n] \n",
    "  \n",
    "    # check convergence, l1 norm \n",
    "    err = sum([abs(x[n] - xlast[n]) for n in x])\n",
    "    #print(err)\n",
    "    #print(N*tol)\n",
    "    if err < N*tol: \n",
    "        #print(x)\n",
    "        break\n",
    "\n",
    "#Check with PageRank Networkx Function\n",
    "#print(Pg)\n",
    "\n",
    "#Display\n",
    "for i in range(len(nodename)):\n",
    "    print(nodename[i],x[i])\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix vector product function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[16  6  8]\n"
     ]
    }
   ],
   "source": [
    "def matrixvectorprod(mat,vect):\n",
    "    return mat.dot(vect)\n",
    "\n",
    "#Test\n",
    "a = np.array([[ 5, 1 ,3], \n",
    "                  [ 1, 1 ,1], \n",
    "                  [ 1, 2 ,1]])\n",
    "b = np.array([1, 2, 3])\n",
    "\n",
    "print(matrixvectorprod(a,b))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Centrality function ???"
   ]
  }
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