From d7afb3cdb02c2a3a02b8fd216b295836d4d1a3a9 Mon Sep 17 00:00:00 2001
From: noah <noah@theschricks.com>
Date: Mon, 24 Jan 2022 23:26:05 -0600
Subject: [PATCH] Submission

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 Schrick-Noah_CS-7863_Homework-1.R | 86 +++++++++++++++++++++++++++++++
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+# 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=" ")
+plot(g, vertex.size = g.deg)
+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)$vector # resolves degree ties
+g.eigs.sorted <- sort(g.eigs,decreasing=T)
+t(t(g.eigs.sorted)) #print one element per line
+sizemult <- 50/g.eigs.sorted[1]
+V(g)$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,)$vector
+g.pr.sorted <- sort(g.pr, decreasing = T)
+t(t(g.pr.sorted))
+sizemult <- 50/g.pr.sorted[1]
+V(g)$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 <- 50/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)
+
+