Submission

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)}
+