SNA_W5&6
楊庭宇_0063
2025-03-24
練習2
- 1.請先使用R繪製下列網絡圖並且將網絡中你覺得比較重要的node(s)用紅色標示出來，試著說明你為什麼覺得這個(些)node(s)重要。
library(igraph)##
## 載入套件：'igraph'## 下列物件被遮斷自 'package:stats':
##
## decompose, spectrum## 下列物件被遮斷自 'package:base':
##
## union# 建立有向圖
gg <- make_graph(
edges = c(3,4, 4,2, 4,5, 1,2, 5,1, 1,5,
1,10, 10,1, 10,6, 6,10, 6,9, 9,6,
7,6, 9,8, 7,8, 7,9),
directed = TRUE
)
# 計算中介中心性
node_centrality <- betweenness(gg, directed = TRUE)
# 找出擁有最大中介中心性的節點
max_centrality <- max(node_centrality)
important_nodes <- which(node_centrality == max_centrality)
# 設定節點顏色
node_colors <- ifelse(seq_along(V(gg)) %in% important_nodes, "red", "gray")
# 繪製圖
plot(gg,
vertex.color = node_colors,
vertex.size = 20,
vertex.label.color = "black",
vertex.label.cex = 1.2,
edge.arrow.size = 0.5
)
# 顯示每個節點的中介中心性
print(node_centrality)## [1] 21 0 0 7 10 18 0 0 6 21網絡中比較重要的node(s)以紅色標示，試說明為什麼這個(些)node(s)重要：
標示紅色之節點在於關注影響力最大的節點，採用中介中心性（Betweenness Centrality） 來判斷重要節點。中介中心性較高的節點，代表它在資訊傳遞中的關鍵程度較高。- 2.請列印出這個網絡的各種資料格式
- adjacency matrix
- Edge(arc) List
- Adjacency List
# 取得鄰接矩陣
adj_matrix <- as_adjacency_matrix(gg, sparse = FALSE)
print(adj_matrix)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 1 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0 0
## [5,] 1 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1 1
## [7,] 0 0 0 0 0 1 0 1 1 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 1 0 1 0 0
## [10,] 1 0 0 0 0 1 0 0 0 0# 取得邊列表
edge_list <- get.edgelist(gg)## Warning: `get.edgelist()` was deprecated in igraph 2.0.0.
## ℹ Please use `as_edgelist()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.print(edge_list)## [,1] [,2]
## [1,] 3 4
## [2,] 4 2
## [3,] 4 5
## [4,] 1 2
## [5,] 5 1
## [6,] 1 5
## [7,] 1 10
## [8,] 10 1
## [9,] 10 6
## [10,] 6 10
## [11,] 6 9
## [12,] 9 6
## [13,] 7 6
## [14,] 9 8
## [15,] 7 8
## [16,] 7 9# 取得鄰接列表
V(gg)$name <- as.character(1:vcount(gg))
adj_list <- lapply(V(gg), function(v) neighbors(gg, v, mode = "out"))
names(adj_list) <- V(gg)$name
print(adj_list)## $`1`
## + 3/10 vertices, named, from 202a53d:
## [1] 2 5 10
##
## $`2`
## + 0/10 vertices, named, from 202a53d:
##
## $`3`
## + 1/10 vertex, named, from 202a53d:
## [1] 4
##
## $`4`
## + 2/10 vertices, named, from 202a53d:
## [1] 2 5
##
## $`5`
## + 1/10 vertex, named, from 202a53d:
## [1] 1
##
## $`6`
## + 2/10 vertices, named, from 202a53d:
## [1] 9 10
##
## $`7`
## + 3/10 vertices, named, from 202a53d:
## [1] 6 8 9
##
## $`8`
## + 0/10 vertices, named, from 202a53d:
##
## $`9`
## + 2/10 vertices, named, from 202a53d:
## [1] 6 8
##
## $`10`
## + 2/10 vertices, named, from 202a53d:
## [1] 1 6練習3
- 1.建立一個由5個nodes組成的網絡，網絡連結為： 1->2, 1->3, 2->4, 3->4, 4->5。
# 建立有向圖
ggg <- make_graph(
edges = c(1,2, 1,3, 2,4, 3,4, 4,5),
directed = TRUE
)
E(ggg)## + 5/5 edges from 20922c4:
## [1] 1->2 1->3 2->4 3->4 4->5- 2.請在這個網絡圖中多增加一個node及與這個node相關的連結： 3->6, 6->5。
library(magrittr)
ggg <- ggg %>% add_vertices(1) %>% add_edges(edges=c(3,6, 6,5))
E(ggg)## + 7/7 edges from 2098341:
## [1] 1->2 1->3 2->4 3->4 4->5 3->6 6->5- 3.將node的名稱命名為A-F。
V(ggg)$name <- c("A", "B", "C", "D", "E", "F")
V(ggg)$name## [1] "A" "B" "C" "D" "E" "F"- 4.繪製這個網絡圖，用不同顏色標示出你覺得這個網絡中比較重要的node(s)。
# 計算中介中心性
node_centrality_2 <- betweenness(ggg, directed = TRUE)
# 找出擁有最大中介中心性的節點
max_centrality_2 <- max(node_centrality_2)
# 設定節點顏色
node_colors_2 <- ifelse(node_centrality_2 == max_centrality_2, "red","gray")
# 繪製圖
plot(ggg,
vertex.color = node_colors_2,
vertex.size = 20,
vertex.label.color = "black",
vertex.label.cex = 1.2,
edge.arrow.size = 0.5
)
# 顯示每個節點的中介中心性
print(node_centrality_2)## A B C D E F
## 0.0000000 0.8333333 2.1666667 2.1666667 0.0000000 0.8333333標示紅色之節點在於關注影響力最大的節點，採用中介中心性（Betweenness Centrality） 來判斷重要節點。中介中心性較高的節點，代表它在資訊傳遞中的關鍵程度較高。