具有孤立頂點/節點的歸一化度中心性度量（r igraph）

Question

我對網絡分析很陌生。 我想用 R 計算歸一化中心性度量（度、介數和特征向量）。 我創建了以下邊緣列表，其中 ID1 和 ID2 都是投資者。 如果 ID1 和 ID2 都填充，投資者共同投資，否則，投資者單獨投資（即孤立節點）：

edgelist <- structure(list(ID1 = c("Cottonwood Capital Partners LLC", "Sequoia Capital Operations LLC", 
                   "Seraphim Capital (General Partner) LLP", "Seraphim Capital (General Partner) LLP", 
                   "Providence Equity Partners LLC", "Turn8", "Matrix Partners LP", 
                   "Zeeuws Investeringsfonds BV", "Venionaire Capital GmbH", "CincyTech", 
                   "First Round Capital", "Matrix Partners LP", "Mohr Davidow Ventures", 
                   "Esprit Capital Partners LLP", "Yaletown Venture Partners", "Wellington Partners", 
                   "Charles River Ventures LLC", "MB VENTURE PARTNERS L L C", "Edison Partners", 
                   "Ballast Point Venture Partners LLC", "Arcview Group", "Foundry Group LLC", 
                   "Sosventures LLC", "Vantagepoint Management Inc", "Bain Capital Venture Partners LLC", 
                   "NAV VC", "Bluerun Ventures LP", "Draper Fisher Jurvetson International Inc", 
                   "Claremont Creek Ventures LP", "Meritage Funds"), ID2 = c("Pangaea Ventures Ltd", 
                                                                             NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "RPM Ventures Management LLC", 
                                                                             NA, "Kennet Partners Ltd", NA, NA, "Gotham Ventures LLC", NA, 
                                                                             NA, NA, "Syncom Management Co Inc", "Lightspeed Venture Partners China Co Ltd", 
                                                                             NA, "First Round Capital", NA)), row.names = c(NA, -30L), class = c("tbl_df", 
                                                                                                                                                 "tbl", "data.frame"))

為了計算歸一化度中心性，我使用以下代碼：

library(igraph)
net <- graph.data.frame(edgelist, directed = F) # create undirected graph

"Warning message:
In graph.data.frame(edgelist, directed = F) :
In `d' `NA' elements were replaced with string "NA""

degree_norm <- degree(net, mode = "all", normalized = T) # retreive normalized degree measure
betw_norm <- betweenness(net2, directed=F, normalized = T) # retreive normalized betw measure
ev <- eigen_centrality(net2, directed = F, scale=F, weights = NULL) # retreive normalized ev

如您所見，出現Warning message ：它將NA視為單獨的投資者（它將NA變為字符串）。 我保持孤立投資者的原因是標准化需要將原始程度度量（使用連接的節點/投資者計算的）除以任何投資者可能投資的投資者的可能數量（即所有可能的投資者，計算那些投資的投資者）獨自的）。

關於如何規避此類問題的任何建議？ 我嘗試使用鄰接矩陣，但也無法弄清楚......

非常感謝！

Answer 1

使用igraph時，處理與其他節點沒有連接的節點的正確方法是傳入一個頂點列表。 使用您提供的數據：

# first get a list of all the nodes, excluding the NA
nodeslist <- data.frame(name= na.omit(unique(c(edgelist$ID1,edgelist$ID2 ))))

# delete the NAs from the edge list
edgelist <- na.omit(edgelist)

# create the `igraph` object
g <- graph_from_data_frame(edgelist,
                           directed = F,
                           vertices = nodeslist)

# compute normalized degree
V(g)$degree <- igraph::degree(g, mode = "all", normalized = T)

# explore the result: there are 34 nodes, and the (not-normalized) degree of all nodes
# is either 0 or 1. Therefore, the normalized degree should be either 1/33=0.03030303 or 0:
V(g)$degree
 [1] 0.03030303 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
 [8] 0.00000000 0.00000000 0.03030303 0.00000000 0.00000000 0.00000000 0.00000000
[15] 0.03030303 0.00000000 0.03030303 0.00000000 0.00000000 0.03030303 0.00000000
[22] 0.00000000 0.00000000 0.03030303 0.03030303 0.00000000 0.03030303 0.00000000
[29] 0.03030303 0.03030303 0.03030303 0.03030303 0.03030303 0.03030303