From c8dabebd87d45b5f5ce6c6106426396742253a75 Mon Sep 17 00:00:00 2001 From: noah Date: Tue, 25 Jan 2022 01:13:36 -0600 Subject: [PATCH] Submission --- Schrick-Noah_CS-7863_Homework-1.R | 181 +++++++++++++++------------- Schrick-Noah_CS-7863_Homework-1.pdf | Bin 0 -> 272153 bytes 2 files changed, 94 insertions(+), 87 deletions(-) create mode 100644 Schrick-Noah_CS-7863_Homework-1.pdf diff --git a/Schrick-Noah_CS-7863_Homework-1.R b/Schrick-Noah_CS-7863_Homework-1.R index b7640b4..d008ed0 100644 --- a/Schrick-Noah_CS-7863_Homework-1.R +++ b/Schrick-Noah_CS-7863_Homework-1.R @@ -1,87 +1,94 @@ -# Homework 1 for the University of Tulsa's CS-7863 Network Theory Course -# Degree, Eigenvector, Katz, and Page Rank Centralities on igraph networks -# Professor: Dr. McKinney, Fall 2021 -# Noah Schrick - 1492657 - -# Imports -#install.packages("igraph") -#install.packages("igraphdata") -library(igraph) -library(igraphdata) -data(karate) -data(yeast) - -# Create our graph object -g <- karate -g.netname <- "karate" -#g <- yeast -#g.netname <- "yeast" -############### Degree ############### - -# Get degree -g.deg <- degree(g) -# Plots -mainname <- paste("Network based on Degree for the", g.netname, "network", sep=" ") -sizemult <- 25/max(g.deg) -plot(g, vertex.size = g.deg*sizemult, main=mainname) -g.hist <- hist(g.deg,-1:max(g.deg),plot=F) -plot(g.hist) - -############### Eigenvector Centrality ############### - -# igraph's eigenvector centrality -g.eigs <- eigen_centrality(g)$vector # resolves degree ties -g.eigs.sorted <- sort(g.eigs,decreasing=T) -t(t(g.eigs.sorted)) #print one element per line -sizemult <- 25/g.eigs.sorted[1] -V(g)$size <- (g.eigs*sizemult) #size the network nodes by eigenvector centrality -mainname <- paste("Network based on Eigenvector Centrality for the", g.netname, "network", sep=" ") -plot(g, main=mainname) - - - -############### Page Rank ############### -# via library: -g.pr <- page.rank(g,)$vector -g.pr.sorted <- sort(g.pr, decreasing = T) -t(t(g.pr.sorted)) -sizemult <- 25/g.pr.sorted[1] -V(g)$size <- (g.pr*sizemult) #size the network nodes by page rank -mainname <- paste("Network based on Page Rank for the", g.netname, "network", sep=" ") -plot(g, main=mainname) - -############### Katz ############### -katz.cent <- function(A, alpha=NULL, beta=NULL){ #NULL sets the default value - if (class(A) == 'igraph'){ - #Error checking. Turn into adj matrix. - A <- get.adjacency(A) - } - - lam.dom <- eigen(A)$values[1] #dom eigenvec - if (is.null(alpha)){ - alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed - } - - n <- nrow(A) - if (is.null(beta)){ - beta <- matrix(rep(1/n, n),ncol=1) - } - - #Katz scores - scores <- solve(diag(n) - alpha*A,beta) - - return(scores) -} - -kcs <- katz.cent(g) # call the function -kcs.df <- data.frame(as.matrix(kcs), row.names = V(g)$name) # add the names -kcs.df <- kcs.df[order(-kcs.df[,1]), , drop = FALSE] # sort by decreasing -kcs.df <- kcs.df/max(kcs.df) # make non-neg -kcs.df - -sizemult <- 25/kcs.df[,1][1] -V(g)$size <- (kcs*sizemult) #size the network nodes by page rank -mainname <- paste("Network based on Katz Centrality for the", g.netname, "network", sep=" ") -plot(g, main=mainname) - - +# Homework 1 for the University of Tulsa's CS-7863 Network Theory Course +# Degree, Eigenvector, Katz, and Page Rank Centralities on igraph networks +# Professor: Dr. McKinney, Fall 2021 +# Noah Schrick - 1492657 + +# Imports +#install.packages("igraph") +#install.packages("igraphdata") +library(igraph) +library(igraphdata) +data(karate) +data(yeast) + +# Create our graph object +g <- karate +g.netname <- "karate" +#g <- yeast +#g.netname <- "yeast" +############### Degree ############### + +# Get degree +g.deg <- degree(g) +# Plots +mainname <- paste("Network based on Degree for the", g.netname, "network", sep=" ") +sizemult <- 25/max(g.deg) +if(g.netname == "yeast"){ + plot(g, vertex.size = g.deg*sizemult, main=mainname, vertex.label=NA) +} else{plot(g, vertex.size = g.deg*sizemult, main=mainname)} +g.hist <- hist(g.deg,-1:max(g.deg),plot=F) +plot(g.hist) + +############### Eigenvector Centrality ############### + +# igraph's eigenvector centrality +g.eigs <- eigen_centrality(g)$vector # resolves degree ties +g.eigs.sorted <- sort(g.eigs,decreasing=T) +t(t(g.eigs.sorted)) #print one element per line +sizemult <- 25/g.eigs.sorted[1] +V(g)$size <- (g.eigs*sizemult) #size the network nodes by eigenvector centrality +mainname <- paste("Network based on Eigenvector Centrality for the", g.netname, "network", sep=" ") +if(g.netname == "yeast"){ + plot(g, main=mainname, vertex.label=NA) +} else{plot(g, main=mainname)} + + + +############### Page Rank ############### +# via library: +g.pr <- page.rank(g,)$vector +g.pr.sorted <- sort(g.pr, decreasing = T) +t(t(g.pr.sorted)) +sizemult <- 25/g.pr.sorted[1] +V(g)$size <- (g.pr*sizemult) #size the network nodes by page rank +mainname <- paste("Network based on Page Rank for the", g.netname, "network", sep=" ") +if(g.netname == "yeast"){ + plot(g, main=mainname, vertex.label=NA) +} else{plot(g, main=mainname)} + +############### Katz ############### +katz.cent <- function(A, alpha=NULL, beta=NULL){ #NULL sets the default value + if (class(A) == 'igraph'){ + #Error checking. Turn into adj matrix. + A <- get.adjacency(A) + } + + lam.dom <- eigen(A)$values[1] #dom eigenvec + if (is.null(alpha)){ + alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed + } + + n <- nrow(A) + if (is.null(beta)){ + beta <- matrix(rep(1/n, n),ncol=1) + } + + #Katz scores + scores <- solve(diag(n) - alpha*A,beta) + + return(scores) +} + +kcs <- katz.cent(g) # call the function +kcs.df <- data.frame(as.matrix(kcs), row.names = V(g)$name) # add the names +kcs.df <- kcs.df[order(-kcs.df[,1]), , drop = FALSE] # sort by decreasing +kcs.df <- kcs.df/max(kcs.df) # make non-neg +kcs.df + +sizemult <- 25/kcs.df[,1][1] +V(g)$size <- (kcs*sizemult) #size the network nodes by page rank +mainname <- paste("Network based on Katz Centrality for the", g.netname, "network", sep=" ") +if(g.netname == "yeast"){ + plot(g, main=mainname, vertex.label=NA) +} else{plot(g, main=mainname)} + diff --git a/Schrick-Noah_CS-7863_Homework-1.pdf b/Schrick-Noah_CS-7863_Homework-1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3b54f915112b8855443da6b176af1e42163b4c09 GIT binary patch literal 272153 zcmd422UL^M(k}cW3ZgVYL8U5Hdhbn;CJIVNnsjLiy@sxUQ~?2{iV7&b2M7d^Cek|? zlF*SFLJJVe4W9FT_niM*_y7L?u65VCEY`}Kch8=gz4y#Bd(Z4}JbR?ZFDxKQagC#v z@JDe?m{o`sZ0$sGO-@cw-`~wnP{qp2$_4Bo_{_?|&XZMy(5x%?#0uoVZ3p5v(0jlt zsORP3ZR4fyVP~fc279rJO8+H!YUSaq39<(h*jzl?*|HMI>=YCPpW1m@*%ElNibzZS zr8IQ3^R@GM=3!@V=V1r3xey}#mxqD^#Wg#S?O$y!^HSIIvhuPcw5#h$vi_Axc#>lMJ7B^b80%O& z+1Xt5*K{RJtFSOD;h(^T(Dcj$Y@=uAWhzKm7(snIKd*m~DF5R_*R z8SH0D=qki2K^V8Bw1_z?VNyU|1f@M$#r|rh?g938BZ&IDnt#6t>Iv$5Sb;p72Cr>XAJ1bX;YkpbHA53)+LN`OvY)guaj)G*maTp)!`LHzM z$Pc%@GB|6Z$|&+bik)}f7z;uhk*Vx=3Nmu5WE@IwV( zNJ2sZrzQ!u0~_HTFI~NHSEjkT#5*G-YM@(ex}82mJH<$=_1nFrAR@WRg@LO3bgzZ2 zy`!y5=qimdse4;30G<&jp=mPiy8;) z40QzN%mqZ~-acUG;`^Xg`Q*XZ7o?q4;?LMc*FSMTl%jgBFpe~Hpm)olzrSu}Z1yCw z*~~6I=}*k`N;>Qrv^LF9ed-XST%B>N(Sz zuiRD23?<5m;e|Vykrj~{d=lr%4-&R$q8?E0wlPGkWiQ@E_M0;oY`?6$Lbf4O&k=kl_R@P&1!IFo99cM#P`m+5Gncn?NXY7K9 zrN7z4V&WuOpQ}EhMlee#s#9)?>~hlSUQ^!pV4tD5Z91&~o+C-_>wINw@pJijV~ab- z$#4AHu>j-7kEr9RAf3uZi+L~NfnPR8SMfu8+hL}Im(Z3T;_g1Bcg{*bQ#=TNZ>RCw z@5{U3*E{VGet!z~nxOo|tWKPsb@kRI91~?RmEp%<>8v%bn~ZLhAv_x@DXT+AZCn;5 zH@a_scF|y^iM4(p4Bi~`@A>>{zB9)EPh_o$Wa6#jIO`IUFsiW~({t6YkDRFESR-l7 zbeG*%7_^)kV#aoEYTxkyojG{lX!aaDFrM|`T+H5|@6RVxa*1rO` z5i69d2PL5}S$W*x&o%?!XTl_#cb6+d1~<(}{{q^7IK+Qo+XaC9hd2Fo(hF=6)bqCX zy1-w30&M<$t8L|KN5C6FWh+m+zZCk8u6CZs`ahqAMMMbQZM|My;P79< zfA#!}7ym`q|H=6;EdEvWzbZ#S2nWv#QJRE+;%M^_8XEX`9FMzRYF2o@Slb#DIrD($u3|IJvS>GyZ;$! z1(hAWJfGQlsDNGFz@WcAAgD=*+#YV=i&)BPZ{^}iaQOdacomis68e7x*bSsSXr{is z+nwn?>D9Q-`=w$0?pnG5hEIq!0XK~DM_L0#{3+l5D>O`<_?pluyq-CXq9O@ zS=8zVn{S&+_F>)EI54h(J}yztl>(=4k7ep{{6PnFc`T73f_w^GNBT0Owe?{QLJ zlN}kCYwYYG>!A5FcDvDZRnz$R({}zM8#0?e%^V~2?#VMjC{))5?|#s?M7u$r(9>S| z%ICua2aD2-gS1KWH@Y4%8VRoZVMWGFouv7^Qqb)K2KLgJD_2W=!#8wdt>VZBzRnL- z@<>lhHjh3T(Nxqe#?iS;>2T1Fg=`KKW;@l~U^h)U`crZ?71s$d3XaUrt--`qqV)7Qkqo!bDQN9T5e7xfBT`3-hf#g=3cu2w|9bT1aa-r zmz@YUtbF-)K$Nw@t?SgrfzcLT3FE<#>--bP=Mf1%&PW52Saa?*L)Eks=B7P9bgyn9 zc1K6`e21enZ}uBuU!x^e0?@OFs{M5NlYna8P1Zl0(5YG2$tzFXOO)a7LEj?OokYx8 zZk(Z$OLrosyT``GWp(FAuhZI5l*ypqO2c+rTi;6AkFiR5|4#{}1AC<1Ep3CyvmzDY zLc*jxkqYXdE%Y7PYuQPQi7`LGZQ&3DraR@=tNiOkSF;~RfLUqLiBV5~RbG1U%~Cam zmH0+mhj`k^7r}4n^FzmA=cB2kOMCpyCkKVv5&a(dYB8eHyQ}%U*TI!Ub~mx|8y%}b z>!X%ePHjwsKRJ~QOp$gsCai!%IwgJ;Src8NO|-o?sdgOC9?A!=|UQ6WoJ1YNXD zf)%P`kd=b?nBuIIV!67KDtHyY39^#10d=Kzm7lZx==~%-9y-!-%Nuz(Vfh_Ird}S@ zYiQ%Oe3x`??4U}fFJLdStY0BfE$#D%CqbWh3?1epZ2B!?H^Eg8X^Mbt# zQb#Y7qV`ylwjrilf0?FM!%Ms+MJ@e1;)k4Bpvc zyq;<;^2!0k(SOJ+T0&lG=;WlBa3OSOpXSWP{ln7%Gl$+m^EYp80(X?M86AaIA}H(5 zPbiX~bzZt$;3DuAtR<+Yd5rpM5PDqN#LYmoi-I2HD4?|$+4qdnYIcT*PDFp z-ms63l<&(%w{zPje#)4#?!W0urY%UG+bGeH+BYA#$ff0Fxc1q+aD8sHSYOt`V|i4| z2z;%Yf;%?|6FQ09@ict6FqI?qtlP+8=W2TPa2*2uGJ;*N5>T=~V2l5@0|3#_5w4yx zP1J21DgZDq79gElCkX&Iin}j+kzV;$_U_XE*~s&MH}~Q_zvpJR_SdcTPFtpUdvgik z+_`!>I-+_R0K#3BLdsQOkj69JC_n6S?)lmz;h@t&m^}CC8B3O`BZpfPD^&QyG7D8~ z(jf`J`U2sDoAy_PTQ;AY-7J3#CQP^f&A~)VGbZyhbqF!=F2?nVVxT*2jb)wz2(@() zfL~phs6U_pls0n8TFhL0pmAi==G15ac;vKux_7*?h1S7s2BFdLApBm7&V}URX^7xK zqU(1{7^0OS{4AD%$2YZHOoM>@9t!Qm3Fr@z!!cPsqd+wpE#9j>vbwc z-`G#|@;SRyz*@u{7B|P{v!1ss2c`h5he#yJ5)OQnDM^567IBHk@Sj9VPT!!Zlr3Wu za-VG#BiFy;f=8qXE2b*es(#X>fQ%pheSX`yG9VT8fwbi>O%EH$evq0JtkaM3F8#>S6wiY=P*@MhIrx@j*KY zEPqqX{Qhd^!bra8Lm%R+s>3P%<8Q&t+`_rJhh>->C`>~87eaP{)u8-QRXKMKOG~{> z&R^pHn9@(; 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