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# 507 Class Note for PHYS 597A with Professor Albert at PSU

Marketplace > Pennsylvania State University > 507 Class Note for PHYS 597A with Professor Albert at PSU

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15
Properties of real networks degree distribution I III HI 1 in lll DII mll Nodes with small degrees are most frequent The fraction of highly connected nodes decreases but is not zero Look closer use a logarithmic plot O 1 3 0 1O 1O 1O 1O 10 5 101 1 0392 semilog 1 03 1 loglog O 4 Plotting power laws and exponentials 06 linear frx we fx 0x71 Note these are plots of functions and not degree 02 distributions fxC X 20 4O 60 80 100 n and outdegree distribution of the VWWV 10 a nodes webpages 1072 a 7 7 edges hyperlinks 1oquot 7 O 7 7 A A Pmk a k 5 2 1076 7 7 5 7 11 of n Pmk at k 10 7 O 7 7 10quot 7 7 7 10712 7 0 2 4 6 2 1o 10 1o 10 1o 10 k Usage he degree distribution scales as a power law R Albert H Jeong AL Barabasi Nature 401 130 1999 A Broder eta Comput Netw 33 309 1999 Degree distributions in networks of science collaborations n Coauthor HEP Coauthor neurosci 10 Hi I i l 39l i I i l i l 1 oquot h A O V 1 o 2 Pk 10 Pkk391392104 7 E 7 Pkk392391 10 5 7 7 7 A em 10 5 i i 10 1o2 i 10510 10 k M E J Newman Phys Rev E 64 016131 2001 AL Barabasi et al condmat101041 62 2001 Powerlaw degree distributions were found in diverse networks internetiruuterievei Aetureuiiaburanun nudes actms w eddes easiieiinw nudes vuutevs m eddes Babies mi in PU ND 39 Pk31kr Pk in k39 m w 39 L mquot iii fii 1nquot 1nx k 1m in 1nx R Gavindan H randrnunarunkiii EEE inieieeirnunnni ArL aaiabasi F39 Aiben Science 286 namiaaa Metabolic networks have a powerlaw degree distribution s 3 ii 1 Amends i m E i i noon 39 V PM kez bipartite nudes metabumESi ieseiidns oeegans i divectedE EESi nut veactantsubs1 at2 1 g n pmddiuiieseiiui H deundeiai Nature AUI aai znun Cleaning up degree distributions orten it is dimeditm deterrninetne best t tn tne puints nat make up a degree distnbunun Metnuds urdata iEanup i iugantnrnie binning bintne K range use bins ufexpunentiaiiy increasing size 2 Dispiay ne umuia WE degree distnbunun Pk K iP c or M PkgtKerkK Ex Determine ne degree distnbdnun and Eumuia WE degree distnbdnun er ne grapn untne rignt Probability that a node has a degree irtne nuncumuiative degree distnbdnun aiigns win a puwer iaw Witn eqmnent vii tne Eumuia ve degree distnbdtinn Wiii aiign Witn a puwer iaw Winn eqmnert dei Dues nutappiy turdii Probability that node has degree x Px m cx Inga Power grid has exponential degree distribution Path length and order in real networks in l 39 m o A m D nodes generators lzufmniw A cc 3 quot Dun power stations xinwergm d X A A u D Acollabomtnnmmrks ms N f n u edges powerlines m gmmmm A 2 i0 i A mmm A A m 2 l i i e E i g a ymaaSulif nomoms of o o P k gt K a exp05K s m r mmm yuxplrllS V l Vii Ht 1 u 11 H7 iif in m39 in in 39 5 5 1 2s E K N 1n if i in in is quot 3 N c c k logk R39 Albert 39 Albert G39 L39 Nakarado39 Phys39 Rev39 E 6939 025103R 2004 Apparent scaling with the network size and average degree as though these different networks were members ofthe same family D b fb 1 Betweenness centrality load distribution of lstn utlon o etweenness centra 1t y the power grld im up Coauthorship v a E b 20gt0LL i7 W 7 r r 7 7 quotquot39 iri Wld 39de Proteininteraction quot 39W39 e e 7 Metabolic netw E lu Internet As level 22 E 39 l Mi p5g g392 Q How doesthe iii i P5g is gquot m i noncumulative 5 m l Iquoti39 distribution quotquot f3 i W V look like in the region W mill where the cumulative W to mquot 10 I0quot 10 it 10 HP 0 distribution is almost E R horizontal K I Goh et 21 PNAS 99 12583 2002 R Albert Abert G L Nakarado Phys Rev E 69 025103R 2004 egree utts Endpumtthh h ang squantt ed by the urre atmn between and h eweraur 21h 21le N EMN EvNJ PEST we curreta EIH e assurta we Negatwe urre atmn e deassurtatwe mm d m normer a ret t m mmtwnd Mme gm a t Eldwmmti WW m Unlversallty In largescale neMOFkS tent mum Mum 1513 me am b ml Mm W mlhbmmmu mm new 020 mm A mm dmm WWW 7671 um am A The degree dethhdtmh ququ a decreasmg mmth usuaHy a We mm mer m 4702 a 1m e mmV Mdn bmkt want 38 a mu t FDWEMaW r m u u l y l mme mm am i The bEMEEnnESS eehtrahty dethbdtmh S atsu decreasmg mm 05 39nr 7 T 2 wed quot t Ehm jmm 3m 3 22 33 Eu h ndtcate heterdgehety and he eXTsterree at hth mm mmm mm 1 m t mmth me new m a em WW l rfjf r ih lffj ft r 6 3339 w The detahees seate uganthmmaHy the hethrh 5sz WWW hm m hwt rd m t mg N Suma netvvurkstend tn be assunatwe technutugmat ahd bm ugma netvvurks tend El be dwsassunatwe Pussmxe eadses uf assurtatmty attrae mm at S mHarS gruup athhatmh Pussmxe eadse uf deassurta thy senTEE reTatmhsths e g dTreetdhes M E J Namnan Phys Rev E Zuni I 10gltkgt The emstehhg uef ment dues hut seerhtd depend uh the netvvurk 5sz and t seerhstd be prdpdmdhaxwth the average degree 0 nck Frequent subgraphs e hut dhwersaT but edrhrhdh tn severaT netvvurks

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