2.1 エッジリストからグラフオブジェクト生成.

• エッジリストをvectorで与える.
  • make_graph ベクトルからグラフ生成.
  • ノードラベルを名に値がわりふられるV(g)$name
• エッジリストをmatrixで与える.
  • graph_from_edgelist(), graph.edgelist()
• エッジリストをdata.frameで与える.
  • graph_from_data_frame()
• 有向, 無向グラフ
  • 無向グラフの場合, 上の関数の引数でdirected =F. デフォルトはT
  • make_directed_graph, make_undirected_graph
• 自己ループと多重ループの削除 simplify

# エッジリストをベクトルで与える.   
v1 <- c("1","2", "1","3", "1","4", "2","3", "3","3","4","2", "2","4")
v2 <- c(1, 2, 1, 3, 1, 4, 2, 3, 3, 3, 4, 2, 2, 4) 

# エッジリストをマトリックスもしくはデータフレームで与える. 
m1 <- matrix(c("A","B", "A","C", "A","D", "B","C", "C","C", "D","B","B","D"), 
             byrow = T, ncol = 2)　
m2 <- matrix(c(1,2, 1,3, 1,4, 2,3, 3,3, 4,2, 2,4), 
             byrow = T, ncol = 2)
d1 <- data.frame(m1, stringsAsFactors = F)


make_graph(v1, directed = F)
make_graph(v2, directed = F)

graph_from_edgelist(m1, directed = F)
graph.edgelist(m2, directed = F)
graph_from_data_frame(d1, directed = F)

## IGRAPH 6808619 UN-- 4 7 -- 
## + attr: name (v/c)
## + edges from 6808619 (vertex names):
## [1] 1--2 1--3 1--4 2--3 3--3 2--4 2--4
## IGRAPH 97801d5 U--- 4 7 -- 
## + edges from 97801d5:
## [1] 1--2 1--3 1--4 2--3 3--3 2--4 2--4
## IGRAPH 9b0de2d UN-- 4 7 -- 
## + attr: name (v/c)
## + edges from 9b0de2d (vertex names):
## [1] A--B A--C A--D B--C C--C B--D B--D
## IGRAPH baf436a U--- 4 7 -- 
## + edges from baf436a:
## [1] 1--2 1--3 1--4 2--3 3--3 2--4 2--4
## IGRAPH 5f8293b UN-- 4 7 -- 
## + attr: name (v/c)
## + edges from 5f8293b (vertex names):
## [1] A--B A--C A--D B--C C--C B--D B--D

2.2 ノード・エッジを直接記述する.

• graph_from_literal
• make_graph(~) リテラルの前に~を書く
• 有向グラフの場合 x-+y のように書く, -の数は無視される x----y

par(mfrow = c(1,3))
plot(graph_from_literal( A-B-C-A, D-C-E, C-G, H ), main = "graph_from_literal")
plot(graph_from_literal( A-+B, B+-C, D-+E-+F, G+-+H, I), main = "graph_from_literal")
plot(make_graph( ~ A-+B, B+-C, D-+E-+F, G+-+H, I), main = "make_graph( ~ )")

2.3 隣接行列からグラフオブジェクトの生成.

• graph_from_adjacency_matrix,graph.adjacency有向グラフの場合, 上三角行列の情報が使われる.
• diag = Fで自己ループを除外
• 正方行列でないとエラー

# 隣接行列の作成
set.seed(1) 
adjm <- matrix(sample(x = 0:1, size = 100, replace = TRUE, prob = c(0.8,0.2)), ncol = 10)

# 隣接行列からグラフオブジェクト作成 
g <- graph_from_adjacency_matrix(adjmatrix = adjm, mode = "undirected", diag = F )

# グラフ描画  
plot(g)

2.4 相関係数行列からグラフの作成.

• 2値データに変換して重みなしグラフを生成
• 相関係数を重みとする

# 相関係数行列を -> 2値データに変換 ->　無向グラフ 
thresh <- 0.7
g1 <- cor(mtcars) %>% 
  {ifelse(. < thresh, 0, 1)} %>% 
  graph_from_adjacency_matrix(., mode = "undirected", diag = F)

# 相関係数行列(spearman) ->　重み付き無向グラフ
g2 <- cor(mtcars, method = "spearman") %>%
  graph_from_adjacency_matrix(., mode = "undirected", weighted = T, diag = F)

# 重みをエッジの幅に反映させる.  相関の正負をエッジの色に反映させる 
ewid <- abs(igraph::E(g2)$weight)*2
ecol <- ifelse(igraph::E(g2)$weight < 0 , "steelblue3", "red")

# グラフ描画
par(mfrow = c(1,2), mar = c(0,0,0,0))
plot(g1, layout = layout_nicely,
     vertex.label.cex = 0.8,
     vertex.frame.color = "white", 
     vertex.size = 10, 
     vertex.color = "lightblue")

plot(g2, layout = layout_in_circle, 
     vertex.label.cex = 0.8,
     vertex.frame.color = "white", 
     vertex.size = 10, 
     vertex.color = "lightblue",
     edge.width = ewid,
     edge.color = ecol)

2.5 make_graphでグラフ名を与えると作られるグラフ.

• make_graphの引数に以下のグラフ名(26ある)を入れると作られる
• 他の引数は無視される.

gs <- c("Bull","Chvatal","Coxeter","Cubical","Diamond","Folkman",
        "Franklin","Frucht","Grotzsch","Heawood","Herschel",
        "House","HouseX","Levi","McGee","Meredith",
        "Noperfectmatching","Nonline","Petersen","Robertson","Smallestcyclicgroup",
        "Thomassen","Tutte","Uniquely3colorable","Walther","Zachary")

par(mfrow = c(3,3), mar = c(1,0,1,0))
invisible(lapply(seq_along(gs), function(i){
  plot(make_graph(gs[i]), vertex.label = NA, main = gs[i])
  }))

2.6 特殊なグラフ.

• make_tree 木, make_star 星, make_ring リング, make_lattice格子
  
• 引数としてノード数, 有向, 無向などを指定する
• make_bipartite_graph 二部グラフ, make_chordal_ring, make_de_bruijn_graphドブリングラフ make_ego_graph, make_empty_graph エッジ無しのグラフ, make_full_graph 完全グラフ, make_full_citation_graph 完全引用グラフ,
• graph_from_atlas「An Atlas of Graphs」にある、7つの頂点を持つすべての無向グラフ(0~1252).

par(mar = c(1,0,1,0), mfrow = c(3,3)) 
plot(make_tree(5), main = "make_tree")                
plot(make_star(5), main = "make_star")                       
plot(make_ring(10), main = "make_ring")                        
plot(make_lattice(c(3,3)), main = "make_lattice") 
plot(make_full_citation_graph(10, directed = F), main = "make_full_citation_graph") 
plot(make_bipartite_graph(rep(0:1, length = 10), c(1:10)), main = "make_bipartite_graph")
plot(graph_from_atlas(100), main = "graph_from_atlas(100)") 

2.7 スケールフリーグラフ, ランダムグラフ.

• sample_pa, barabasi.game　スケールフリーグラフ. ノード数とエッジ数
• make_full_graph, graph.full 完全グラフ. ノード数を指定する.
• sample_gnp, sample_gnm,erdos.renyi.game,random.graph.game　ランダムグラフ. すべての可能なエッジが一定確率で作成. 確率もしくはエッジ数を指定する. G(n, p), G(n, m)

par(mar = c(0,0,1,0), mfrow = c(1,3))

# スケールフリーグラフ 
plot(sample_pa(n = 20, power = 1, directed = F), main = "'sample_pa' scale free graph")

# 完全グラフ
plot(make_full_graph(20), main = "'make_full_graph' complete graph")

# ランダムグラフ(ノード50個、p = 0.1)
plot(sample_gnp(n = 20, p = 0.1, direct = F), main = "'sample_gnp' random graph p = 0.1")

3.1 gml形式のファイル読み込み.

• read_graph(file, format), read.graph(file, format)
• グラフフォーマット“pajek”, “ncol”, “lgl”, “graphml”,　“dimacs”, “graphdb”, “gml”, “dl”

# gml形式の読み込み　
g <- read_graph("~/pub/sampledata/dataset/network/gml/lesmis.gml", format = "gml") 
 
# ノードラベル  
V(g)$label %>% head 

# weight
E(g)$value %>% head 

# 書き出し
write_graph(graph = g, file = "./graph.txt", format = "edgelist")
　

5.1 グラフ描画.

• ?plot.igraph, ?igraph.plotting で詳細なhelpを見る.

# グラフ
set.seed(1) 
g <- random.graph.game(n = 20, p = 0.1, directed = F)　%>%
  set_vertex_attr(., name = "label", value = LETTERS[1:vcount(.)]) %>% 
  set_edge_attr(., name = "label", value = 1:ecount(.)) 
 

# 描画
par(mar = c(0,0,1,0))
plot(g, 
     layout = layout_with_fr,
     vertex.color = "navy", # sort(unique(degree(g)))[factor(degree(g))] + 1,
     vertex.frame.color = "white", 
     vertex.label = V(g)$label,
     vertex.label.color = "white",
     vertex.label.cex = 1,
     vertex.label.dist = 0,
     vertex.label.family = "Helvetica",
     vertex.label.font = 2,  # 1:plane, 2:bold, 3:italic, 4:bolditalic, 5:symbol
     vertex.size = (degree(g) + 5)*2, # 次数を反映させる
     vertex.size2 = 10, # shapeでrectangleを選んだ場合の高さ
     vertex.shape = "rectangle", # circle,square,csquare,rectangle,crectangle,vrectangle,none
     edge.color = "grey",
     edge.width = 2,
     edge.arrow.size = 0.1,
     edge.arrow.width = 3, # 1:solid, 2:dashed, 3:dotted, 4:dotdash, 5:longdash, 6:twodash.
     edge.label.cex = 0.8,
     edge.label.color = "red",
     edge.label.family = "Helvetica",
     edge.label.font = 2,
     edge.lty = 2,
     main = "layout_with_fr"
     )

5.2 コミュニティーごとに色分け.

# コミュニティー検出
cl.lv <- cluster_louvain(g)　

# コミュニティーごとのノードの色、次数が0のノードは同色 
v.c <- RColorBrewer::brewer.pal(n = max(cl.lv$membership), name = "Set2")[cl.lv$membership] %>% 
  ifelse(degree(g) == 0, "grey", .)

# 描画
plot(g, vertex.color = v.c) 

5.3 サークルレイアウトで次数の大きい順に配置layout_in_circle(g, order).

• ノードの配置をorderで変える

lay.crc <- layout_in_circle(g, order = order(degree(g), decreasing = T))
plot(g, layout = lay.crc)

5.4 色々なレイアウト関数. layout_*

# グラフレイアウト関数
lays <- grep("^layout_.+", 
             unclass(utils::lsf.str(envir = asNamespace("igraph"), all = T)), value = T)

# 全部のlayout関数を試す.
par(mfrow = c(3,3))
suppressWarnings(
  for (x in lays) {
    possibleError <- tryCatch({
      coords <- do.call(x, list(g))
      par(mar = c(0,0,1,0))
      plot(g, layout = coords,
           vertex.label = V(g)$name, 
           vertex.label.color = "black",
           vertex.frame.color = "white",
           vertex.label.cex = 1, 
           vertex.size = 15, 
           vertex.color = "lightblue",
           vertex.label.family = "Helvetica", 
           vertex.shape = "circle",
           edge.label = NA,
           edge.color = "gray80", 
           edge.width = 1, 
           edge.lty = 1,
           main = x)
      },
      error = function(e) {
        print(paste("Error in layout ",x,sep = ""))
      })
    if (inherits(possibleError, "error")) next
    }
  )

## [1] "Error in layout layout_as_bipartite"
## [1] "Error in layout layout_modifier"
## [1] "Error in layout layout_spec"
## [1] "Error in layout layout_with_sugiyama"

6.1 ノード数, エッジ数, 連結成分.

• ノード数, エッジ数, 次数vcount, ecount, degree
• ノードラベル V(g)$name
• 隣接ノード adjacent_vertices, V(g)[nei(1)], neighbors(g, 1)
• エッジの重み(weight = Tにした場合) E(g)$weight
• エッジのid get.edge.ids

# グラフ
g <- graph.atlas(100);  V(g)$name <- LETTERS[1:6] 
 
# ノード数、エッジ数, 次数, 隣接ノード
V(g); E(g) # ノード, エッジ
vcount(g); ecount(g) # ノード数, エッジ数 
degree(g) # ノードごとの次数(各頂点が連結している辺の数)
adjacent_vertices(g, 1); V(g)[nei(1)];　neighbors(g, 1) # 隣接ノード

6.2 エッジリスト, 隣接リスト, 隣接行列　取り出し.

• エッジリスト(matrix) as_edgelist, get.edgelist,
• エッジリスト(data.frame) as_data_frame, get.data.frame. dplyr::as_data_frameと区別する. エッジの属性値も出してくれる. what ="vertices"にすればノード属性値のデータフレームを返す. what ="both"では両方
• 隣接リストas_adj_list,get.adjlist
• 隣接行列 as_adjacency_matrix, get.adjacency

as_edgelist(g) # エッジリスト(matrix)
igraph::as_data_frame(g) # エッジリスト(data.frame)
igraph::as_data_frame(g, what = "both")
as_adj_list(g) # 隣接リスト(頂点同士の隣接関係を確認する)
as_adjacency_matrix(g)[1:6,1:6] # 隣接行列

6.3 ノード, エッジの追加・削除.

• disjoint, %du% 2つ以上のグラフを結合(union)する.
  
• add_vertices, add.vertices　ノードの追加
• add_edges, add.edges　エッジの追加
• delete_vertices, delete.vertices ノード削除. 非連結成分を削除する場合 delete_vertices(g, V(g)$name[degree(g)==0])
• delete_edges エッジの削除(エッジのidで指定)

# 3つの完全グラフの和集合 
g <- disjoint_union(make_full_graph(4), make_full_graph(4), make_full_graph(4))

#ノードの追加  
g1 <- add_vertices(graph = g, nv = 3) 

# エッジの追加（ノード1,6間, 1,11間, 6,11間にエッジを追加する） 
g2 <- add_edges(g1, c(1,6, 1,11, 6,11, 4,13, 8,14))  

# エッジの削除 (エッジのidで指定する)
g3 <- delete_edges(g2, get.edge.ids(g, c(2,4, 6,7, 9,12 )))

# 非連結成分の削除
g4 <- delete_vertices(g3, V(g3)[degree(g3) == 0])

# 非連結成分の削除, 連結成分ごとに分割,
gcs <- delete_vertices(g1, V(g1)[degree(g1) == 0]) %>% decompose()


# グラフ描画 
par(mfrow = c(2,3), c(0,0,1,0))
plot(g)  
plot(g1, main = "add_vertices")
plot(g2, main = "add_edges")
plot(g3, main = "delete_edges")
plot(g4, main = "delete_vertices")

# 連結成分ごとに描画
par(mfrow = c(1,3), mar = c(0,0,1,0))

invisible(lapply(gcs, function(x)plot(x)))

6.4 ノード, エッジの属性値を追加.

• 属性値の名前は自由につけられる.　set_vertex_attr, set_edge_attr
• 属性値を確認graph_attr(g)

attr_g <- make_ring(10) %>%
  set_vertex_attr("label", value = LETTERS[1:10]) %>%
  set_edge_attr("label", value = 1:10) 

vertex_attr(attr_g)
edge_attr(attr_g)

plot(attr_g)

## $label
##  [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J"
## 
## $label
##  [1]  1  2  3  4  5  6  7  8  9 10

6.5 連結成分を分割.

• 連結成分の確認. components, clusters
• 連結成分ごとに分割 decompose, decompose.graph. その際min.verticesで連結成分のノード数指定
  • ノード数2以上の連結成分のリストdecompose(g, min.vertices = 2)

set.seed(1) 
g <- random.graph.game(n = 20, p = 0.1, directed = F)　%>%
  set_vertex_attr(., name = "label", value = LETTERS[1:vcount(.)])

# 連結成分の確認
# # membership: 各ノードが属している連結成分, csize:連結成分のサイズ, no:連結成分の数
(cmp <- components(g))

# 連結成分ごとに分割decompose (リストが返る)
dg <- decompose(g, min.vertices = 2)

par(mfrow = c(1, cmp$no))
invisible(lapply(dg, function(x)plot(x)))

# 連結成分のなかにある指定ノードを含むグラフを抽出
v <- c("L", "S")
sub_dg <- sapply(dg, function(x) if(any(V(x)$label %in% v)){x}else{NULL})
l_sub_dg <- sub_dg[!sapply(sub_dg, is.null)]

par(mfrow = c(1, cmp$no))

invisible(lapply(l_sub_dg, function(x)plot(x)))

## $membership
##  [1] 1 1 1 1 1 1 2 3 2 1 2 2 2 1 1 2 1 1 4 2
## 
## $csize
## [1] 11  7  1  1
## 
## $no
## [1] 4

6.6 サブグラフ.

• 指定ノードのみからなるサブグラフinduced_subgraph
• ego_size, ego, make_ego_graph
• subgraph_centrality

g <- make_graph(c("A","B", "A","C", "D","E", "F","G", "H","I"), directed = F)
 
# 指定ノードのみのサブグラフ
subv <- c('A','C','H') 
g2 <- induced_subgraph(graph = g, vids = subv)

# 指定ノードと接続しているノードを含めたサブグラフ
subg <- function(x, subv){
  deg <- decompose(x, mode = "weak")
  
  vnei <- unique(unlist(sapply(deg, FUN = function(s){
    if (any(V(s)$name %in% subv)) V(s)$name else NULL})))
  
  induced_subgraph(graph = g, vids = vnei)
}
g3 <- subg(g, subv)


par(mfrow = c(1,3))
plot(g)
plot(g2, main = "sub-graph with selected node")
plot(g3, main = "sub-graph with connected node")

g <- make_ring(8)
V(g)$name <- c("A", "B", "C", "D", "E", "F", "G", "H")
subg <- make_ego_graph(g, nodes = subv)
invisible(lapply(subg, plot))

g <- make_ring(10)
ego_size(g, 0, 1:3)
ego_size(g, 1, 1:3)
ego_size(g, 2, 1:3)
ego(g, 0, 1:3)
ego(g, 1, 1:3)
ego(g, 2, 1:3)

# attributes are preserved
V(g)$name <- c("a", "b", "c", "d", "e", "f", "g", "h", "i", "j")
make_ego_graph(g, 2, 1:3)

# connecting to the neighborhood
g <- make_ring(10)
g <- connect(g, 2)

## [1] 1 1 1
## [1] 3 3 3
## [1] 5 5 5
## [[1]]
## + 1/10 vertex, from a206d30:
## [1] 1
## 
## [[2]]
## + 1/10 vertex, from a206d30:
## [1] 2
## 
## [[3]]
## + 1/10 vertex, from a206d30:
## [1] 3
## 
## [[1]]
## + 3/10 vertices, from a206d30:
## [1]  1  2 10
## 
## [[2]]
## + 3/10 vertices, from a206d30:
## [1] 2 1 3
## 
## [[3]]
## + 3/10 vertices, from a206d30:
## [1] 3 2 4
## 
## [[1]]
## + 5/10 vertices, from a206d30:
## [1]  1  2 10  3  9
## 
## [[2]]
## + 5/10 vertices, from a206d30:
## [1]  2  1  3 10  4
## 
## [[3]]
## + 5/10 vertices, from a206d30:
## [1] 3 2 4 1 5
## 
## [[1]]
## IGRAPH 8c88f9b UN-- 5 4 -- Ring graph
## + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
## + edges from 8c88f9b (vertex names):
## [1] a--b b--c a--j i--j
## 
## [[2]]
## IGRAPH e2b7e1f UN-- 5 4 -- Ring graph
## + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
## + edges from e2b7e1f (vertex names):
## [1] a--b b--c c--d a--j
## 
## [[3]]
## IGRAPH d1d9de5 UN-- 5 4 -- Ring graph
## + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
## + edges from d1d9de5 (vertex names):
## [1] a--b b--c c--d d--e