# Homework 3 for the University of Tulsa' s CS-7863 Network Theory Course
# Network Clustering
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657

# Imports
library(igraph)
library(igraphdata)
library(WGCNA)

data(karate)
data(yeast)

g1 <- karate
g1.netname <- "Karate"
g2 <- yeast
g2.netname <- "Yeast"

##################### Part 1: Laplace Spectral Clustering #####################
g1.adj <- get.adjacency(g1) # get adjacency
g2.adj <- get.adjacency(g2)
g1.deg <- rowSums(as.matrix(g1.adj)) # get degrees
g2.deg <- rowSums(as.matrix(g2.adj))
g1.Lap <- diag(g1.deg) - g1.adj # L = D-A
g2.Lap <- diag(g2.deg) - g2.adj
n1 <- length(V(g1)) # number of nodes
n2 <- length(V(g2))

# get eigvals and vecs
x1 <- eigen(g1.Lap)$vectors[,n1-1]
x2 <- eigen(g2.Lap)$vectors[,n2-1]
x1_val <- eigen(g1.Lap)$values[n1-1]
x2_val <- eigen(g2.Lap)$values[n2-1]
names(x1) <- names(V(g1))
names(x2) <- names(V(g2))
x1
x2
x1_clusters <- ifelse(x1>0,1,-1)
x2_clusters <- ifelse(x2>0,1,-1)

# Plotting
V(g1)$color <- ifelse(x1_clusters>0,"green","yellow")
#V(g1)$size <- 80*abs(x1)
V(g2)$color <- ifelse(x2_clusters>0,"green","yellow")
V(g2)$size <- 10
plot(g1, main=paste(g1.netname, " Laplace Spectral Clustering"))
plot(g2, main=paste(g2.netname, " Laplace Spectral Clustering"),
     vertex.label=NA)


########################## Part 2: Newman Modularity ##########################


##################### Part 3: Recursive Newman Modularity #####################
# Using igraph
karate.modularity <- fastgreedy.community(karate,merges=TRUE, modularity=TRUE, membership=TRUE)
#memberships <-community.to.membership(karate, karate.modularity$merges, 
  # steps=which.max(fgreedy$modularity)-1)
karate.modularity$membership
karate.modularity$merges
membership.ids <- unique(karate.modularity$membership)
membership.ids
cat(paste('Number of detected communities =',length(membership.ids)))
cat("community sizes: ")
sapply(membership.ids,function(x) {sum(x==karate.modularity$membership)})
cat("modularity: ")
max(karate.modularity$modularity)
#karate.modularity$modularity

V(karate)$color[karate.modularity$membership==1] <- "green"
V(karate)$color[karate.modularity$membership==2] <- "red"
V(karate)$color[karate.modularity$membership==3] <- "blue"

plot(karate,vertex.size=10,
     vertex.label=V(karate)$label,vertex.color=V(karate)$color,
     main=paste("Karate Recursive Newman Modularity"))


###################### Part 4: TOM and Dynamic Tree Cut ######################
# Next smallest eig
y1 <- eigen(g1.Lap)$vectors[,n1-2] # get n-2 column
names(y1) <- names(V(g1))
y1_val <- eigen(g1.Lap)$values[n1-2]
y2 <- eigen(g2.Lap)$vectors[,n2-2] # get n-2 column
names(y2) <- names(V(g2))
y2_val <- eigen(g2.Lap)$values[n2-2]

# Distance in the 2D Laplacian Eig-Space
lap_dist1 <- dist(cbind(x1,y1))
lap_dist2 <- dist(cbind(x2,y2))

# Use hierachical clustering of distance matrix
lap_tree1 <- hclust(lap_dist1)
lap_tree2 <- hclust(lap_dist2)

# Use WGCNA to dynamically decide how many clusters
cutreeDynamicTree(lap_tree1)
cutreeDynamicTree(lap_tree2)

# TOM
g1.TOM <- TOMsimilarity(as.matrix(g1.adj))
g2.TOM <- TOMsimilarity(as.matrix(g2.adj))
g1.TOM
g2.TOM
TOMplot(g1.TOM, lap_tree1, main=paste(g1.netname, " Heatmap Plot"))
TOMplot(g2.TOM, lap_tree2, main=paste(g2.netname, " Heatmap Plot"))

################################ Part 5: UMAP ################################