使用 igraph 在 bipartite.networks 上工作：基本度量的问题（密度、归一化程度）

Question

我是 bipartite.network 分析的新手，我在基本测量方面遇到了一些麻烦。 我正在尝试在不投影 1-mode graphs 的情况下处理 bipartite.networks 。 我的问题来自igraph package 允许创建二分图但这些措施似乎不适应这些图的特殊性。

所以，我的一般问题是当你直接在 bipartite.networks 上工作时你会怎么做？

这是一个密度的具体例子

## Working with an incidence matrix (sample) with 47 columns and 10 rows (unweighted / undirected)
# Want to compute basic global index like density with igraph
library(igraph)
g <- graph.incidence(m, directed = F )
graph.density(g) # result = 0.04636591

# Now trying to compute basic density for a bipartite graph without igraph (number of edges divided  by the product of the two types of vertices)
library(Matrix)
d <- nnzero(m)/ (ncol(m)*nrow(m)) # result 0.1574468

# It seems that bipartite package does the job 
library(bipartite)

networklevel(m, index=c("connectance")) # result 0.1574468

但是二分法package 是非常特定于生态学领域的，很多措施都是针对食物 web 和物种之间的相互作用而设计的（有些，比如聚类系数，似乎没有考虑到图的二分法性质：例如计算 4-周期）。

那么，是否有更简单的方法可以使用igraph在 bipartite.networks 上工作？ 要测量一些全局指标（密度、4 周期的聚类系数，我知道.net 会这样做，但我的实际网络太大），并在考虑二分特异性的情况下标准化局部指标，如度数、紧密度、中间性中心性（就像 Borgatti SP, Everett MG, 1997, « 2-mode data 的网络分析 », Social Networks）？

任何建议将被认真考虑 ！

在代码下面重现我的矩阵“m”的样本

 m <- structure(c(1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 
1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 
0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 
0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0), .Dim = c(10L, 47L), .Dimnames = list(
    c("02723", "13963", "F3238", "02194", "15051", "04477", "02164", 
    "06283", "04080", "08304"), c("1185241", "170063", "10350868", 
    "217831", "2210247", "2262963", "1816670", "1848354", "2232593", 
    "146214", "1880252", "2261639", "2262581", "2158177", "1850147", 
    "2262912", "146412", "2262957", "1566083", "1841811", "146384", 
    "216281", "2220957", "1846986", "1951567", "1581130", "105343", 
    "1580240", "170654", "1796236", "1835553", "1835848", "146400", 
    "1174872", "1283240", "2253354", "1283617", "146617", "160263", 
    "2263115", "184745", "1809858", "1496747", "10346824", "148730", 
    "2262582", "146268")))

Answer 1

密度：你已经知道了

度数 degv1 <- 度数 (g, V(g)[type == FALSE]) degv2 <- 度数 (g, V(g)[type == TRUE])

归一化度数：除以其他节点类别的vcount

degnormv1 <- degv1/length(V(g)[type == TRUE]) degnormv2 <- degv2/length(V(g)[type == FALSE])

没有关于亲密度、介数或聚类系数的答案

Answer 2

对于归一化程度，这里有一个没有 igraph 的解决方案

normalizedegreeV1 <- data.frame(ND = colSums(m)/nrow(m))

normalizedegreeV2 <- data.frame(ND = rowSums(m)/ncol(m))

但这留下了关于中心性措施的其他问题......