Added code and data

1 percolate.R

+# Percolate network created using edges and different distance thresholds
+
+#install.packages(pacman)
+pacman::p_load(foreign, igraph, parallel, dplyr)
+
+print("Creating general graph...")
+edges.dbf <- read.dbf("data/edges.dbf")
+near <- edges.dbf["NEAR_FID"]
+target <- near %>% mutate(target = lag(NEAR_FID))
+target$NEAR_FID <- NULL
+edges.dbf <- cbind(edges.dbf,target)
+edges.dbf$idsec <- rep(c(2, 1), times = length(near$NEAR_FID)/2)
+
+edges_comp <- as.data.frame(subset(edges.dbf, idsec==1, select=c(IN_FID, NEAR_FID, target, Shape_Leng)))
+colnames(edges_comp) <- c("edge_id", "source", "target", "weight")
+edges <- edges_comp[c(2,3,4,1)]
+general.graph.mx <- graph.data.frame(edges, directed = F)
+
+if (!dir.exists("results")) {dir.create("results")}
+
+getSizeDiameter <- function(i, decomposed) {
+  # return cluster size and diameter
+  return (c(length(V(decomposed[[i]])),
+            diameter(decomposed[[i]], directed = FALSE)))
+}
+
+percolate <- function(threshold){
+  start_time <- Sys.time()
+  print(paste0("Processing ", threshold))
+  print("Reducing graph")
+  sub.g = subgraph.edges(general.graph.mx, 
+                         E(general.graph.mx)[E(general.graph.mx)$weight <= threshold], del=T)
+  sub.g <- delete_edges(sub.g, E(sub.g)[E(sub.g)$weight > threshold])
+  sub.g <- delete_vertices(sub.g, degree(sub.g, mode = "total")==0)
+  
+  components <- components(sub.g)
+  
+  sub.g.csize <- induced.subgraph(sub.g, V(sub.g)[components$csize[components$membership]>=50])
+  print("Decomposing graph")
+  decomposed <- decompose.graph(sub.g.csize)
+  
+  cl.list <- seq(1, components(sub.g.csize)$no)
+  
+  cl = parallel::makeCluster(parallel::detectCores()-1)
+  parallel::setDefaultCluster(cl)
+  print(cl)
+  
+  clusterEvalQ(cl, library(igraph))
+  
+  clusterExport(cl, varlist = c("getSizeDiameter"), envir = environment())
+  
+  print(paste0("Working on ", length(cl.list), " clusters..."))
+  out <- parLapplyLB(cl, cl.list, getSizeDiameter, decomposed)
+  
+  out <- data.frame(matrix(unlist(out), nrow=length(cl.list), byrow=T))
+  
+  # return cluster size and diameter
+  names(out) <- c("csize","diameter")
+  
+  stopCluster(cl)
+  
+  end_time <- Sys.time()
+  print(end_time - start_time)
+  saveRDS(out, file = paste0("results/perc.diam", threshold,".Rds"))
+}
+
+print("Ready. Use perc.diam<d> <- percolate(d) to generate one run or lapply on a sequence...")

2 cluster_sizes.R

+# Calculate cluster sizes on network created using edges and different distance thresholds
+# Do not consider graph diameter
+
+pacman::p_load(foreign, igraph, parallel, dplyr)
+
+if (!dir.exists("results")) {dir.create("results")}
+
+if (!exists("edges.dbf")){
+  print("Creating general graph...")
+  edges.dbf <- read.dbf("data/edges.dbf")
+  near <- edges.dbf["NEAR_FID"]
+  target <- near %>% mutate(target = lag(NEAR_FID))
+  target$NEAR_FID <- NULL
+  edges.dbf <- cbind(edges.dbf,target)
+  edges.dbf$idsec <- rep(c(2, 1), times = length(near$NEAR_FID)/2)
+  
+  edges_comp <- as.data.frame(subset(edges.dbf, idsec==1, select=c(IN_FID, NEAR_FID, target, Shape_Leng)))
+  colnames(edges_comp) <- c("edge_id", "source", "target", "weight")
+  edges <- edges_comp[c(2,3,4,1)]
+  general.graph.mx <- graph.data.frame(edges, directed = F)
+}
+
+getSize <- function(i, decomposed) {
+  # return cluster size 
+  return (length(V(decomposed[[i]])))
+}
+
+percolateSize <- function(threshold) {
+  partial_start_time <- Sys.time()
+  print(paste0("Processing ", threshold))
+  print("Percolating graph for current distance...")
+  sub.g = subgraph.edges(general.graph.mx, 
+                         E(general.graph.mx)[E(general.graph.mx)$weight <= threshold], del=T)
+  sub.g <- delete_edges(sub.g, E(sub.g)[E(sub.g)$weight > threshold])
+  sub.g <- delete_vertices(sub.g, degree(sub.g, mode = "total")==0)
+  
+  components <- components(sub.g)
+  
+  sub.g.csize <- induced.subgraph(sub.g, V(sub.g)[components$csize[components$membership]>=50])
+  print("Decomposing graph for cluster sizes >= 50")
+  decomposed <- decompose.graph(sub.g.csize)
+  
+  cl.list <- seq(1, components(sub.g.csize)$no)
+  
+  print(paste0("Working on ", length(cl.list), " clusters..."))
+  out <- invisible(lapply(cl.list, getSize, decomposed))
+  out <- data.frame(matrix(unlist(out), nrow=length(cl.list), byrow=T))
+  
+  # return cluster size 
+  names(out) <- c("csize")
+  
+  saveRDS(out, file = paste0("results/cl-size", threshold,".Rds"))
+  partial_end_time <- Sys.time()
+  print(partial_end_time - partial_start_time)
+}
+
+print("Ready. Use clsize<d> <- percolateSize(d) to generate one run or lapply on a sequence...")

3 entropy.R

+# Calculate and plot Shannon's entropy for different distance thresholds
+
+pacman::p_load(foreign, igraph, parallel, dplyr)
+
+print("Reading input edge and vertex data...")
+
+if (!exists("edges.dbf")){
+  print("Creating general graph...")
+  edges.dbf <- read.dbf("data/edges.dbf")
+  near <- edges.dbf["NEAR_FID"]
+  target <- near %>% mutate(target = lag(NEAR_FID))
+  target$NEAR_FID <- NULL
+  edges.dbf <- cbind(edges.dbf,target)
+  edges.dbf$idsec <- rep(c(2, 1), times = length(near$NEAR_FID)/2)
+  
+  edges_comp <- as.data.frame(subset(edges.dbf, idsec==1, select=c(IN_FID, NEAR_FID, target, Shape_Leng)))
+  colnames(edges_comp) <- c("edge_id", "source", "target", "weight")
+  edges <- edges_comp[c(2,3,4,1)]
+}
+
+if (!exists("nodes")){
+  nodes <- read.csv("data/nodes.csv")
+}
+nodes <- nodes[c(1,1,2,3)]
+colnames(nodes) <- c("id", "node_id", "lng", "lat")
+
+print("Creating general graph...")
+
+general.graph.mx <- graph.data.frame(edges, directed = F, vertices = nodes)
+
+# percolate cluster sizes keeping all clusters - for entropy plot
+percolate_sizes <- function(threshold){
+  current_distance <<- threshold
+  print(paste0("Working on ", threshold))
+  print("Reducing graph")
+  sub.g = subgraph.edges(general.graph.mx, 
+                         E(general.graph.mx)[E(general.graph.mx)$weight <= threshold], del=T)
+  sub.g <- delete_edges(sub.g, E(sub.g)[E(sub.g)$weight > threshold])
+  sub.g <- delete_vertices(sub.g, degree(sub.g, mode = "total")==0)
+  
+  components <- components(sub.g)
+  
+  sub.g.csize <- induced.subgraph(sub.g, V(sub.g)[components$csize[components$membership]>=50])
+  
+  print("Getting components and membership")
+  components <- components(sub.g.csize)
+  
+  # size df
+  sizec <- data.frame(components[["csize"]])
+  sizec$id <- seq(1:length(sizec$components...csize...))
+  colnames(sizec) <- c("csize", "membership")
+  sizec <- sizec[order(-sizec$csize),]
+  sizec$rank <- seq(1:length(sizec$csize))
+  
+  print("Writing output files...")
+  saveRDS(sizec, file = paste0("results/entropy", threshold,".Rds"))
+}
+
+print("Ready. Use entropy<d> <- percolate_sizes(d) to generate one run or lapply on a sequence...")

README.md

 # percolation
 
-City percolation
\ No newline at end of file
+City percolation code in R.
+
+Use `1 percolate.R` to percolate network created using edges and different distance thresholds.
+
+Use `2 cluster_sizes.R` to calculate cluster sizes on network created using edges and different distance thresholds without considering graph diameter.
+
+Use `3 entropy.R` to calculate and plot Shannon's entropy for different distance thresholds.
+
+Results are written to a `results` folder created during runtime if it does not already exist.
\ No newline at end of file

percolation.Rproj

+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX