feat-louvain_community_detection

Author: ArpitaHanjagi

Desktop/open-source/R/graph_algorithms/louvain_community_detection.r

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+# Louvain Method for Community Detection
+#
+# Detects communities (clusters) in a weighted or unweighted undirected graph.
+# It optimizes modularity by iteratively merging nodes into communities
+# to maximize modularity gain.
+
+louvain_community <- function(graph, max_iter = 100) {
+  num_vertices <- max(as.numeric(names(graph)))
+  community <- 1:num_vertices
+  
+  modularity <- function(graph, community) {
+    m <- 0
+    e_in <- 0
+    deg <- rep(0, length(graph))
+    
+    for (i in names(graph)) {
+      deg[i] <- sum(graph[[i]])
+      m <- m + sum(graph[[i]])
+    }
+    m <- m / 2
+    
+    for (i in names(graph)) {
+      for (j in graph[[i]]) {
+        if (community[as.numeric(i)] == community[j]) {
+          e_in <- e_in + 1
+        }
+      }
+    }
+    e_in <- e_in / 2
+    Q <- e_in / m - sum(sapply(unique(community), function(c) {
+      sum(deg[community == c]) / (2*m)
+    })^2)
+    return(Q)
+  }
+  
+  for (iter in 1:max_iter) {
+    changed <- FALSE
+    for (i in 1:num_vertices) {
+      best_comm <- community[i]
+      best_gain <- 0
+      comms <- unique(community)
+      for (c in comms) {
+        temp_comm <- community
+        temp_comm[i] <- c
+        gain <- modularity(graph, temp_comm) - modularity(graph, community)
+        if (gain > best_gain) {
+          best_gain <- gain
+          best_comm <- c
+        }
+      }
+      if (community[i] != best_comm) {
+        community[i] <- best_comm
+        changed <- TRUE
+      }
+    }
+    if (!changed) break
+  }
+  
+  return(community)
+}
+
+# Example usage
+cat("=== Louvain Method for Community Detection ===\n")
+
+# Example undirected graph as adjacency list
+# 1-2, 1-3, 2-3, 2-4, 3-4, 4-5
+louvain_graph <- list(
+  "1" = c(2,3),
+  "2" = c(1,3,4),
+  "3" = c(1,2,4),
+  "4" = c(2,3,5),
+  "5" = c(4)
+)
+
+cat("Graph (adjacency list):\n")
+for (v in names(louvain_graph)) {
+  cat("Vertex", v, "-> [", paste(louvain_graph[[v]], collapse = ", "), "]\n")
+}
+
+cat("\nDetecting communities:\n")
+communities <- louvain_community(louvain_graph)
+for (i in 1:length(communities)) {
+  cat("Vertex", i, "-> Community", communities[i], "\n")
+}