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
+# Homework 1 for the University of Tulsa's CS-7863 Network Theory Course
-# Degree, Eigenvector, Katz, and Page Rank Centralities on igraph networks
+# Degree, Eigenvector, Katz, and Page Rank Centralities on igraph networks
-# Professor: Dr. McKinney, Fall 2021
+# Professor: Dr. McKinney, Fall 2021
-# Noah Schrick - 1492657
+# Noah Schrick - 1492657
-
+
-# Imports
+# Imports
-#install.packages("igraph")
+#install.packages("igraph")
-#install.packages("igraphdata")
+#install.packages("igraphdata")
-library(igraph)
+library(igraph)
-library(igraphdata)
+library(igraphdata)
-data(karate)
+data(karate)
-data(yeast)
+data(yeast)
-
+
-# Create our graph object
+# Create our graph object
-g <- karate
+g <- karate
-g.netname <- "karate"
+g.netname <- "karate"
-#g <- yeast
+#g <- yeast
-#g.netname <- "yeast"
+#g.netname <- "yeast"
-############### Degree ############### 
+############### Degree ############### 
-
+
-# Get degree
+# Get degree
-g.deg <- degree(g)
+g.deg <- degree(g)
-# Plots
+# Plots
-mainname <- paste("Network based on Degree for the", g.netname, "network", sep=" ")
+mainname <- paste("Network based on Degree for the", g.netname, "network", sep=" ")
-sizemult <- 25/max(g.deg)
+sizemult <- 25/max(g.deg)
-plot(g, vertex.size = g.deg*sizemult, main=mainname)
+if(g.netname == "yeast"){
-g.hist <- hist(g.deg,-1:max(g.deg),plot=F)
+  plot(g, vertex.size = g.deg*sizemult, main=mainname, vertex.label=NA)
-plot(g.hist)
+} else{plot(g, vertex.size = g.deg*sizemult, main=mainname)}
-
+g.hist <- hist(g.deg,-1:max(g.deg),plot=F)
-############### Eigenvector Centrality ############### 
+plot(g.hist)
-
+
-# igraph's eigenvector centrality
+############### Eigenvector Centrality ############### 
-g.eigs <- eigen_centrality(g)$vector # resolves degree ties
+
-g.eigs.sorted <- sort(g.eigs,decreasing=T)
+# igraph's eigenvector centrality
-t(t(g.eigs.sorted)) #print one element per line
+g.eigs <- eigen_centrality(g)$vector # resolves degree ties
-sizemult <- 25/g.eigs.sorted[1]
+g.eigs.sorted <- sort(g.eigs,decreasing=T)
-V(g)$size <- (g.eigs*sizemult) #size the network nodes by eigenvector centrality 
+t(t(g.eigs.sorted)) #print one element per line
-mainname <- paste("Network based on Eigenvector Centrality for the", g.netname, "network", sep=" ")
+sizemult <- 25/g.eigs.sorted[1]
-plot(g, main=mainname)
+V(g)$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)
-############### Page Rank ############### 
+} else{plot(g, main=mainname)}
-# via library:
+
-g.pr <- page.rank(g,)$vector
+
-g.pr.sorted <- sort(g.pr, decreasing = T)
+
-t(t(g.pr.sorted))
+############### Page Rank ############### 
-sizemult <- 25/g.pr.sorted[1]
+# via library:
-V(g)$size <- (g.pr*sizemult) #size the network nodes by page rank 
+g.pr <- page.rank(g,)$vector
-mainname <- paste("Network based on Page Rank for the", g.netname, "network", sep=" ")
+g.pr.sorted <- sort(g.pr, decreasing = T)
-plot(g, main=mainname)
+t(t(g.pr.sorted))
-
+sizemult <- 25/g.pr.sorted[1]
-############### Katz ############### 
+V(g)$size <- (g.pr*sizemult) #size the network nodes by page rank 
-katz.cent <- function(A, alpha=NULL, beta=NULL){ #NULL sets the default value
+mainname <- paste("Network based on Page Rank for the", g.netname, "network", sep=" ")
-    if (class(A) == 'igraph'){
+if(g.netname == "yeast"){
-        #Error checking. Turn into adj matrix.
+  plot(g, main=mainname, vertex.label=NA)
-        A <- get.adjacency(A)
+} else{plot(g, main=mainname)}
-    }
+
-    
+############### Katz ############### 
-    lam.dom <- eigen(A)$values[1] #dom eigenvec
+katz.cent <- function(A, alpha=NULL, beta=NULL){ #NULL sets the default value
-    if (is.null(alpha)){
+  if (class(A) == 'igraph'){
-        alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed
+    #Error checking. Turn into adj matrix.
-    }
+    A <- get.adjacency(A)
-    
+  }
-    n <- nrow(A)
+  
-    if (is.null(beta)){
+  lam.dom <- eigen(A)$values[1] #dom eigenvec
-        beta <- matrix(rep(1/n, n),ncol=1)
+  if (is.null(alpha)){
-    }
+    alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed
-    
+  }
-    #Katz scores
+  
-    scores <- solve(diag(n) - alpha*A,beta)
+  n <- nrow(A)
-   
+  if (is.null(beta)){
-    return(scores)
+    beta <- matrix(rep(1/n, n),ncol=1)
-}
+  }
-
+  
-kcs <- katz.cent(g) # call the function
+  #Katz scores
-kcs.df <- data.frame(as.matrix(kcs), row.names = V(g)$name) # add the names
+  scores <- solve(diag(n) - alpha*A,beta)
-kcs.df <- kcs.df[order(-kcs.df[,1]), , drop = FALSE] # sort by decreasing
+  
-kcs.df <- kcs.df/max(kcs.df) # make non-neg
+  return(scores)
-kcs.df
+}
-
+
-sizemult <- 25/kcs.df[,1][1]
+kcs <- katz.cent(g) # call the function
-V(g)$size <- (kcs*sizemult) #size the network nodes by page rank 
+kcs.df <- data.frame(as.matrix(kcs), row.names = V(g)$name) # add the names
-mainname <- paste("Network based on Katz Centrality for the", g.netname, "network", sep=" ")
+kcs.df <- kcs.df[order(-kcs.df[,1]), , drop = FALSE] # sort by decreasing
-plot(g, main=mainname)
+kcs.df <- kcs.df/max(kcs.df) # make non-neg
-
+kcs.df
-
+
+sizemult <- 25/kcs.df[,1][1]
+V(g)$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)}
+