455 lines
17 KiB
R
455 lines
17 KiB
R
# Final Project for the University of Tulsa's CS-7863 Network Theory Course
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# Compliance Graph Analysis
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# Professor: Dr. McKinney, Spring 2022
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# Noah L. Schrick - 1492657
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library(igraph)
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library(centiserve)
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library(RBGL)
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library(DirectedClustering)
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################## Read in the previously generated networks ##################
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setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
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source("./CG_Files/manual_import.R")
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car <- import_networks(1)
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car.netname <- "Vehicle Maintenance"
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hipaa <- import_networks(2)
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hipaa.netname <- "HIPAA Compliance"
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pci <- import_networks(3)
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pci.netname <- "PCI Compliance"
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# Get basic network attributes
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car.adj <- get.adjacency(car)
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car.deg <- rowSums(as.matrix(car.adj)) # degree
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car.n <- length(V(car))
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hipaa.adj <- get.adjacency(hipaa)
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hipaa.deg <- rowSums(as.matrix(hipaa.adj)) # degree
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hipaa.n <- length(V(hipaa))
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pci.adj <- get.adjacency(pci)
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pci.deg <- rowSums(as.matrix(pci.adj)) # degree
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pci.n <- length(V(pci))
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############################# Base Centralities #############################
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source("centralities.R")
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base_centralities <- matrix(list(), nrow=3, ncol=5)
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rownames(base_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(base_centralities) <- c("Degree", "Katz", "Page Rank", "K-path", "Betweenness")
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### Degree
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base_centralities[[1,1]] <- car.deg %>% sort(decreasing = T)
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base_centralities[[2,1]] <- hipaa.deg %>% sort(decreasing = T)
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base_centralities[[3,1]] <- pci.deg %>% sort(decreasing = T)
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#### Katz
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car.katz <- katz.cent(car)
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nodes <- car.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- car.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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base_centralities[[1,2]] <- car.katz[rowSums(apply(car.katz,2,is.nan))==0,] %>% sort(decreasing = T)
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base_centralities[[2,2]] <- katz.cent(hipaa) %>% sort(decreasing = T)
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hipaa.katz <- katz.cent(hipaa)
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nodes <- hipaa.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- hipaa.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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base_centralities[[3,2]] <- katz.cent(pci) %>% sort(decreasing = T)
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pci.katz <- katz.cent(pci)
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nodes <- pci.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- pci.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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### Page Rank
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base_centralities[[1,3]] <- page.rank(car)$vector %>% sort(decreasing = T)
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base_centralities[[2,3]] <- page.rank(hipaa)$vector %>% sort(decreasing = T)
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base_centralities[[3,3]] <- page.rank(pci)$vector %>% sort(decreasing = T)
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### K-path
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base_centralities[[1,4]] <- geokpath(car, V(car), "out") %>% sort(decreasing = T)
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base_centralities[[2,4]] <- geokpath(hipaa, V(hipaa), "out") %>% sort(decreasing = T)
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base_centralities[[3,4]] <- geokpath(pci, V(pci), "out") %>% sort(decreasing = T)
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### Betweenness
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base_centralities[[1,5]] <- betweenness(car, TRUE) %>% sort(decreasing = T)
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base_centralities[[2,5]] <- betweenness(hipaa, TRUE) %>% sort(decreasing = T)
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base_centralities[[3,5]] <- betweenness(pci, TRUE) %>% sort(decreasing = T)
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############################### Base Clustering ###############################
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source("self_newman_mod.R")
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base_clusters <- matrix(list(), nrow=3, ncol=2)
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rownames(base_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(base_centralities) <- c("Laplace", "CG")
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### Laplacian
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car.Lap <- diag(car.deg) - car.adj # L = D-A
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hipaa.Lap <- diag(hipaa.deg) - hipaa.adj
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pci.Lap <- diag(pci.deg) - pci.adj
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# get eigvals and vecs
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car.eigs <- Re(eigen(car.Lap)$vectors[,car.n-1])
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car.eig_val <- eigen(car.Lap)$values[car.n-1]
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names(car.eigs) <- names(V(car))
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car.l_clusters <- ifelse(car.eigs>0,1,-1)
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base_clusters[[1,1]] <- car.l_clusters
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V(car)$color <- ifelse(car.l_clusters>0, "green", "yellow")
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plot(car, main=paste(car.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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hipaa.eigs <- Re(eigen(hipaa.Lap)$vectors[,hipaa.n-1])
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hipaa.eig_val <- eigen(hipaa.Lap)$values[hipaa.n-1]
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names(hipaa.eigs) <- names(V(hipaa))
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hipaa.l_clusters <- ifelse(hipaa.eigs>0,1,-1)
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base_clusters[[2,1]] <- hipaa.l_clusters
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V(hipaa)$color <- ifelse(hipaa.l_clusters>0, "green", "yellow")
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plot(hipaa, main=paste(hipaa.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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pci.eigs <- Re(eigen(pci.Lap)$vectors[,pci.n-1])
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pci.eig_val <- eigen(pci.Lap)$values[pci.n-1]
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names(pci.eigs) <- names(V(pci))
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pci.l_clusters <- ifelse(pci.eigs>0,1,-1)
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base_clusters[[3,1]] <- pci.l_clusters
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V(pci)$color <- ifelse(pci.l_clusters>0, "green", "yellow")
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plot(pci, main=paste(pci.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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### Clemente and Grassi
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base_clusters[[1,2]] <- ClustBCG(as.matrix(car.adj), "directed")$totalCC
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base_clusters[[2,2]] <- ClustBCG(as.matrix(hipaa.adj), "directed")$totalCC
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base_clusters[[3,2]] <- ClustBCG(as.matrix(pci.adj), "directed")$totalCC
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################################ Misc Analysis ################################
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min_cut(car,"0", "2490")
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min_cut(hipaa,"0","2320")
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min_cut(pci,"0","60")
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max_flow(car, "0", "2490")
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max_flow(hipaa,"0","2320")
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max_flow(pci,"0","60")
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### Transitive closure
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car.graph <- as_graphnel(car)
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hipaa.graph <- as_graphnel(hipaa)
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pci.graph <- as_graphnel(pci)
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car.tc <- graph_from_graphnel(transitive.closure(car.graph))
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hipaa.tc <- graph_from_graphnel(transitive.closure(hipaa.graph))
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pci.tc <- graph_from_graphnel(transitive.closure(pci.graph))
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### Edge connectivty
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edge_connectivity(car, "0", "2490")
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edge_connectivity(hipaa,"0","2320")
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edge_connectivity(pci,"0","60")
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# Dominator Tree
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car.dtree <- dominator_tree(car, "0", "out")$domtree
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hipaa.dtree <- dominator_tree(hipaa, "0", "out")$domtree
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pci.dtree <- dominator_tree(pci, "0", "out")$domtree
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###################### Transitive Closure Centralities ######################
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tc_centralities <- matrix(list(), nrow=3, ncol=5)
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rownames(tc_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(tc_centralities) <- c("Degree", "Katz", "Page Rank", "K-path", "Betweenness")
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# Get basic network attributes
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car.tc.adj <- get.adjacency(car.tc)
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car.tc.deg <- rowSums(as.matrix(car.tc.adj)) # degree
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car.tc.n <- length(V(car.tc))
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hipaa.tc.adj <- get.adjacency(hipaa.tc)
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hipaa.tc.deg <- rowSums(as.matrix(hipaa.tc.adj)) # degree
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hipaa.tc.n <- length(V(hipaa.tc))
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pci.tc.adj <- get.adjacency(pci.tc)
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pci.tc.deg <- rowSums(as.matrix(pci.tc.adj)) # degree
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pci.tc.n <- length(V(pci.tc))
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### Degree
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tc_centralities[[1,1]] <- car.tc.deg %>% sort(decreasing = T)
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tc_centralities[[2,1]] <- hipaa.tc.deg %>% sort(decreasing = T)
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tc_centralities[[3,1]] <- pci.tc.deg %>% sort(decreasing = T)
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#### Katz
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car.tc.katz <- katz.cent(car.tc)
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tc_centralities[[1,2]] <- car.tc.katz[rowSums(apply(car.tc.katz,2,is.nan))==0,] %>% sort(decreasing = T)
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car.tc.katz <- katz.cent(car.tc)
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nodes <- car.tc.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- car.tc.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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tc_centralities[[2,2]] <- katz.cent(hipaa.tc) %>% sort(decreasing = T)
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hipaa.tc.katz <- katz.cent(hipaa.tc)
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nodes <- hipaa.tc.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- hipaa.tc.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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tc_centralities[[3,2]] <- katz.cent(pci.tc) %>% sort(decreasing = T)
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pci.tc.katz <- katz.cent(pci.tc)
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nodes <- pci.tc.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- pci.tc.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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### Page Rank
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tc_centralities[[1,3]] <- page.rank(car.tc)$vector %>% sort(decreasing = T)
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tc_centralities[[2,3]] <- page.rank(hipaa.tc)$vector %>% sort(decreasing = T)
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tc_centralities[[3,3]] <- page.rank(pci.tc)$vector %>% sort(decreasing = T)
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### K-path
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tc_centralities[[1,4]] <- geokpath(car.tc, V(car.tc), "out") %>% sort(decreasing = T)
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tc_centralities[[2,4]] <- geokpath(hipaa.tc, V(hipaa.tc), "out") %>% sort(decreasing = T)
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tc_centralities[[3,4]] <- geokpath(pci.tc, V(pci.tc), "out") %>% sort(decreasing = T)
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### Betweenness
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tc_centralities[[1,5]] <- betweenness(car.tc, TRUE) %>% sort(decreasing = T)
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tc_centralities[[2,5]] <- betweenness(hipaa.tc, TRUE) %>% sort(decreasing = T)
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tc_centralities[[3,5]] <- betweenness(pci.tc, TRUE) %>% sort(decreasing = T)
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######################## Transitive Closure Clustering ########################
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source("self_newman_mod.R")
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tc_clusters <- matrix(list(), nrow=3, ncol=2)
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rownames(tc_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(tc_centralities) <- c("Laplace", "CG")
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### Laplacian
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car.tc.Lap <- diag(car.tc.deg) - car.tc.adj # L = D-A
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hipaa.tc.Lap <- diag(hipaa.tc.deg) - hipaa.tc.adj
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pci.tc.Lap <- diag(pci.tc.deg) - pci.tc.adj
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# get eigvals and vecs
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car.tc.eigs <- Re(eigen(car.tc.Lap)$vectors[,car.tc.n-1])
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car.tc.eig_val <- eigen(car.tc.Lap)$values[car.tc.n-1]
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names(car.tc.eigs) <- names(V(car.tc))
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car.tc.l_clusters <- ifelse(car.tc.eigs>0,1,-1)
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tc_clusters[[1,1]] <- car.tc.l_clusters
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V(car.tc)$color <- ifelse(car.tc.l_clusters>0, "green", "yellow")
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plot(car.tc, main=paste(car.tc.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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hipaa.tc.eigs <- Re(eigen(hipaa.tc.Lap)$vectors[,hipaa.tc.n-1])
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hipaa.tc.eig_val <- eigen(hipaa.tc.Lap)$values[hipaa.tc.n-1]
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names(hipaa.tc.eigs) <- names(V(hipaa.tc))
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hipaa.tc.l_clusters <- ifelse(hipaa.tc.eigs>0,1,-1)
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tc_clusters[[2,1]] <- hipaa.tc.l_clusters
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V(hipaa.tc)$color <- ifelse(hipaa.tc.l_clusters>0, "green", "yellow")
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plot(hipaa.tc, main=paste(hipaa.tc.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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pci.tc.eigs <- Re(eigen(pci.tc.Lap)$vectors[,pci.tc.n-1])
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pci.tc.eig_val <- eigen(pci.tc.Lap)$values[pci.tc.n-1]
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names(pci.tc.eigs) <- names(V(pci.tc))
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pci.tc.l_clusters <- ifelse(pci.tc.eigs>0,1,-1)
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tc_clusters[[3,1]] <- pci.tc.l_clusters
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V(pci.tc)$color <- ifelse(pci.tc.l_clusters>0, "green", "yellow")
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plot(pci.tc, main=paste(pci.tc.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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### Clemente and Grassi
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tc_clusters[[1,2]] <- ClustBCG(as.matrix(car.tc.adj), "directed")$totalCC
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tc_clusters[[2,2]] <- ClustBCG(as.matrix(hipaa.tc.adj), "directed")$totalCC
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tc_clusters[[3,2]] <- ClustBCG(as.matrix(pci.tc.adj), "directed")$totalCC
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######################### Dominant Tree Centralities #########################
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dtree_centralities <- matrix(list(), nrow=3, ncol=5)
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rownames(dtree_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(dtree_centralities) <- c("Degree", "Katz", "Page Rank", "K-path", "Betweenness")
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# Get basic network attributes
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car.dtree.adj <- get.adjacency(car.dtree)
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car.dtree.deg <- rowSums(as.matrix(car.dtree.adj)) # degree
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car.dtree.n <- length(V(car.dtree))
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hipaa.dtree.adj <- get.adjacency(hipaa.dtree)
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hipaa.dtree.deg <- rowSums(as.matrix(hipaa.dtree.adj)) # degree
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hipaa.dtree.n <- length(V(hipaa.dtree))
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pci.dtree.adj <- get.adjacency(pci.dtree)
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pci.dtree.deg <- rowSums(as.matrix(pci.dtree.adj)) # degree
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pci.dtree.n <- length(V(pci.dtree))
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### Degree
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dtree_centralities[[1,1]] <- car.dtree.deg %>% sort(decreasing = T)
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dtree_centralities[[2,1]] <- hipaa.dtree.deg %>% sort(decreasing = T)
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dtree_centralities[[3,1]] <- pci.dtree.deg %>% sort(decreasing = T)
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#### Katz
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car.dtree.katz <- katz.cent(car.dtree)
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dtree_centralities[[1,2]] <- car.dtree.katz[rowSums(apply(car.dtree.katz,2,is.nan))==0,] %>% sort(decreasing = T)
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car.dtree.katz <- katz.cent(car.dtree)
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nodes <- car.dtree.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- car.dtree.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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dtree_centralities[[2,2]] <- katz.cent(hipaa.dtree) %>% sort(decreasing = T)
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hipaa.dtree.katz <- katz.cent(hipaa.dtree)
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nodes <- hipaa.dtree.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- hipaa.dtree.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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dtree_centralities[[3,2]] <- katz.cent(pci.dtree) %>% sort(decreasing = T)
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pci.dtree.katz <- katz.cent(pci.dtree)
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nodes <- pci.dtree.katz %>% order(decreasing=T)
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nodes <- head(nodes, 15)-1
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vals <- pci.dtree.katz %>% sort(decreasing=T)
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vals <- head(vals, 15)
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### Page Rank
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dtree_centralities[[1,3]] <- page.rank(car.dtree)$vector %>% sort(decreasing = T)
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dtree_centralities[[2,3]] <- page.rank(hipaa.dtree)$vector %>% sort(decreasing = T)
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dtree_centralities[[3,3]] <- page.rank(pci.dtree)$vector %>% sort(decreasing = T)
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### K-path
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dtree_centralities[[1,4]] <- geokpath(car.dtree, V(car.dtree), "out") %>% sort(decreasing = T)
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dtree_centralities[[2,4]] <- geokpath(hipaa.dtree, V(hipaa.dtree), "out") %>% sort(decreasing = T)
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dtree_centralities[[3,4]] <- geokpath(pci.dtree, V(pci.dtree), "out") %>% sort(decreasing = T)
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### Betweenness
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dtree_centralities[[1,5]] <- betweenness(car.dtree, TRUE) %>% sort(decreasing = T)
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dtree_centralities[[2,5]] <- betweenness(hipaa.dtree, TRUE) %>% sort(decreasing = T)
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dtree_centralities[[3,5]] <- betweenness(pci.dtree, TRUE) %>% sort(decreasing = T)
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########################## Dominant Tree Clustering ##########################
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source("self_newman_mod.R")
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dtree_clusters <- matrix(list(), nrow=3, ncol=2)
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rownames(dtree_centralities) <- c(car.netname, hipaa.netname, pci.netname)
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colnames(dtree_centralities) <- c("Laplace", "CG")
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### Laplacian
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car.dtree.Lap <- diag(car.dtree.deg) - car.dtree.adj # L = D-A
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hipaa.dtree.Lap <- diag(hipaa.dtree.deg) - hipaa.dtree.adj
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pci.dtree.Lap <- diag(pci.dtree.deg) - pci.dtree.adj
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# get eigvals and vecs
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car.dtree.eigs <- Re(eigen(car.dtree.Lap)$vectors[,car.dtree.n-1])
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car.dtree.eig_val <- eigen(car.dtree.Lap)$values[car.dtree.n-1]
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names(car.dtree.eigs) <- names(V(car.dtree))
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car.dtree.l_clusters <- ifelse(car.dtree.eigs>0,1,-1)
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dtree_clusters[[1,1]] <- car.dtree.l_clusters
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V(car.dtree)$color <- ifelse(car.dtree.l_clusters>0, "green", "yellow")
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plot(car.dtree, main=paste(car.dtree.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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hipaa.dtree.eigs <- Re(eigen(hipaa.dtree.Lap)$vectors[,hipaa.dtree.n-1])
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hipaa.dtree.eig_val <- eigen(hipaa.dtree.Lap)$values[hipaa.dtree.n-1]
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names(hipaa.dtree.eigs) <- names(V(hipaa.dtree))
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hipaa.dtree.l_clusters <- ifelse(hipaa.dtree.eigs>0,1,-1)
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dtree_clusters[[2,1]] <- hipaa.dtree.l_clusters
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V(hipaa.dtree)$color <- ifelse(hipaa.dtree.l_clusters>0, "green", "yellow")
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plot(hipaa.dtree, main=paste(hipaa.dtree.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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pci.dtree.eigs <- Re(eigen(pci.dtree.Lap)$vectors[,pci.dtree.n-1])
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pci.dtree.eig_val <- eigen(pci.dtree.Lap)$values[pci.dtree.n-1]
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names(pci.dtree.eigs) <- names(V(pci.dtree))
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pci.dtree.l_clusters <- ifelse(pci.dtree.eigs>0,1,-1)
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dtree_clusters[[3,1]] <- pci.dtree.l_clusters
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V(pci.dtree)$color <- ifelse(pci.dtree.l_clusters>0, "green", "yellow")
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plot(pci.dtree, main=paste(pci.dtree.netname, "Laplace Spectral Clustering"), vertex.label=NA)
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### Clemente and Grassi
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dtree_clusters[[1,2]] <- ClustBCG(as.matrix(car.dtree.adj), "directed")$totalCC
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dtree_clusters[[2,2]] <- ClustBCG(as.matrix(hipaa.dtree.adj), "directed")$totalCC
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dtree_clusters[[3,2]] <- ClustBCG(as.matrix(pci.dtree.adj), "directed")$totalCC
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############################# Write Final Results #############################
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write.table(base_centralities, file='results.csv')
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write.table(tc_centralities, file='results.csv')
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write.table(dtree_centralities, file='results.csv')
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### Degree:
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head(base_centralities[[1,1]], 15) #Car
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head(tc_centralities[[1,1]],15)
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head(dtree_centralities[[1,1]],15)
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head(base_centralities[[2,1]], 15) #HIPAA
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head(tc_centralities[[2,1]],15)
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head(dtree_centralities[[2,1]],15)
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head(base_centralities[[3,1]], 15) #PCI
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head(tc_centralities[[3,1]],15)
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head(dtree_centralities[[3,1]],15)
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### Katz:
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head(base_centralities[[1,2]], 15) #Car
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head(tc_centralities[[1,2]],15)
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head(dtree_centralities[[1,2]],15)
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head(base_centralities[[2,2]], 15) #HIPAA
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head(tc_centralities[[2,2]],15)
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head(dtree_centralities[[2,2]],15)
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head(base_centralities[[3,2]], 15) #PCI
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head(tc_centralities[[3,2]],15)
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head(dtree_centralities[[3,2]],15)
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### Page Rank:
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head(base_centralities[[1,3]], 15) #Car
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head(tc_centralities[[1,3]],15)
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head(dtree_centralities[[1,3]],15)
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head(base_centralities[[2,3]], 15) #HIPAA
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head(tc_centralities[[2,3]],15)
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head(dtree_centralities[[2,3]],15)
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head(base_centralities[[3,3]], 15) #PCI
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head(tc_centralities[[3,3]],15)
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head(dtree_centralities[[3,3]],15)
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### K-Path:
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head(base_centralities[[1,4]], 15) #Car
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head(tc_centralities[[1,4]],15)
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head(dtree_centralities[[1,4]],15)
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head(base_centralities[[2,4]], 15) #HIPAA
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head(tc_centralities[[2,4]],15)
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head(dtree_centralities[[2,4]],15)
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head(base_centralities[[3,4]], 15) #PCI
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head(tc_centralities[[3,4]],15)
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head(dtree_centralities[[3,4]],15)
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### Betweenness:
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head(base_centralities[[1,5]], 15) #Car
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head(tc_centralities[[1,5]],15)
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head(dtree_centralities[[1,5]],15)
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head(base_centralities[[2,5]], 15) #HIPAA
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head(tc_centralities[[2,5]],15)
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head(dtree_centralities[[2,5]],15)
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head(base_centralities[[3,5]], 15) #PCI
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head(tc_centralities[[3,5]],15)
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head(dtree_centralities[[3,5]],15)
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### Laplacian:
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head(base_clusters[[1,1]], 15) #Car
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head(tc_centralities[[1,1]],15)
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head(dtree_centralities[[1,1]],15)
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head(base_clusters[[2,1]], 15) #HIPAA
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head(tc_centralities[[2,1]],15)
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head(dtree_centralities[[2,1]],15)
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head(base_clusters[[3,1]], 15) #PCI
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head(tc_centralities[[3,1]],15)
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head(dtree_centralities[[3,1]],15)
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### CG:
|
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head(base_clusters[[1,2]], 15) #Car
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head(tc_centralities[[1,2]],15)
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head(dtree_centralities[[1,2]],15)
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head(base_clusters[[2,2]], 15) #HIPAA
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head(tc_centralities[[2,2]],15)
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head(dtree_centralities[[2,2]],15)
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head(base_clusters[[3,2]], 15) #PCI
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head(tc_centralities[[3,2]],15)
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head(dtree_centralities[[3,2]],15)
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