用R确定随机图中的切割和桥接

Question

我有这个生成随机图的代码， 如何识别图表中的桥梁和切口

library(igraph)
G <- graph( c(1,2,1,3,1,4,3,4,3,5,5,6,6,7,7,8,8,9,3,8,5,8,10,1,10,2,11,2,12,1,13,4,13,7,14,2,15,6,16,7,17,8,19,13,18,4,19,7), directed = FALSE )
# Assign attributes to the graph
G$name    <- "A colorful example graph"
# Assign attributes to the graph's vertices
V(G)$name  <- toupper(letters[1:20])
V(G)$color <- sample(rainbow(20),20,replace=FALSE)
# Assign attributes to the edges
E(G)$weight <- runif(length(E(G)),.3,2)
# Plot the graph -- details in the "Drawing graphs" section of the igraph manual
plot(G, layout = layout.fruchterman.reingold, 
     main = G$name,
     vertex.label = V(G)$name,
     vertex.size = 15,
     vertex.color= V(G)$color,
     vertex.frame.color= "white",
     vertex.label.color = "white",
     vertex.label.family = "sans",
     edge.width=E(G)$weight, 
     edge.color="black")

Answer 1

好的，鉴于我已经能够根据您的定义使用术语来辨别，这可能是一种让您实现目标的方法。希望它在某种程度上有所帮助，虽然它肯定不是最有效的桥梁寻找算法（迭代去除边缘和计算图形分解），它可以相对较好地适用于小图形。如果您需要更高效的东西，您可能需要手动编写Trajan或其他有效算法：

library(igraph)

G <- graph( c(1,2,1,3,1,4,3,4,3,5,5,6,6,7,7,8,8,9,3,8,5,8,10,1,10,2,11,2,12,1,13,4,13,7,14,2,15,6,16,7,17,8,19,13,18,4,19,7), directed = FALSE )

# Assign attributes to the graph
G$name    <- "A graph with articulated.nodes and bridges highlighted"

# Assign attributes to the graph's vertices
V(G)$name  <- toupper(letters[1:20])
V(G)$color <- sample(rainbow(20),20,replace=FALSE)

# Assign attributes to the edges
E(G)$weight <- runif(length(E(G)),.3,2)

##  Set normal vertices to black:
V(G)$color <- "black"

##  Set articulation points to red:
V(G)$color[ articulation.points(G) ] <- "red"

##  Set normal edges to black:
E(G)$color <- "black"

##  Set bridge edges to red:
num_comp <- length( decompose.graph(G) )
for (i in 1:length(E(G))) {
  G_sub <- delete.edges(G, i)
  if ( length( decompose.graph(G_sub) ) > num_comp ) E(G)$color[i] <- "red"
}

plot(G, layout = layout.fruchterman.reingold, 
     main = G$name,
     vertex.label = V(G)$name,
     vertex.size = 15,
     vertex.color= V(G)$color,
     vertex.frame.color= "white",
     vertex.label.color = "white",
     vertex.label.family = "sans",
     edge.width=E(G)$weight, 
     edge.color=E(G)$color)

Answer 2

似乎没有实施。如上所述here，您可以从函数开始实现Trajan's algorithm以查找生成树：

minimum.spanning.tree

至于剪辑，相同的来源指向与您的不同的定义，但您可能想要查看它。