正确使用和解释"modularity()" [英] the correct use and interpretation of `modularity()`

问题描述

在igraph ?modularity部分中，示例代码为

In the igraph ?modularity section there is example code given as

g <- graph.full(5) %du% graph.full(5) %du% graph.full(5)
g <- add.edges(g, c(1,6, 1,11, 6, 11))
wtc <- walktrap.community(g)
modularity(wtc)
#[1] 0.5757575
modularity(g, membership(wtc))
#[1] 0.5757576

wtc的输出显示:

wtc
#Graph community structure calculated with the walktrap algorithm
#Number of communities (best split): 3 
#Modularity (best split): 0.5757575 
#Membership vector:
# [1] 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2

我对不同的部分感到困惑

I am confused by the different parts:

modularity(wtc)
# and
modularity(g, membership(wtc))

wtc本身已经具有最好的拆分及其相关的模块性.为什么在wtc上调用modularity? modularity(g, membership(wtc))我发现正在找到特定的预先选择的拆分的模块化，这对我来说更有意义(在这种情况下，最好的拆分).

wtc itself already has the best split and its associated modularity. why call modularity on wtc? modularity(g, membership(wtc)) I see is finding the modularity of a particular pre chosen split, which makes more sense to me (in this case the best split).

您期望在什么情况下这些结果会有所不同，以及为什么会如此?

In what cases would you expect these results to differ and why e.g.

g2 <- structure(list(from = structure(c(2L, 3L, 4L, 1L, 3L, 4L, 1L, 
  2L, 4L, 1L, 2L, 3L), .Label = c("A", "B", "C", "D"), class = "factor"), 
      to = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 
      4L, 4L), .Label = c("A", "B", "C", "D"), class = "factor"), 
      weight = c(2L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L
      )), .Names = c("from", "to", "weight"), row.names = c(2L, 
  3L, 4L, 5L, 7L, 8L, 9L, 10L, 12L, 13L, 14L, 15L), class = "data.frame")

g2 <- graph.data.frame(g2, vertices = unique(g2[1]))

set.seed(444)
wtc2 <- walktrap.community(g2)
modularity(wtc2)
# [1] 0.4444444
wtc2
# Graph community structure calculated with the walktrap algorithm
# Number of communities (best split): 2 
# Modularity (best split): 0.4444444 
# Membership vector:
# B C D A 
# 2 1 1 2 
modularity(g2, membership(wtc2))
# [1] -0.1666667

sessionInfo()
# R version 3.0.2 (2013-09-25)
# Platform: x86_64-apple-darwin10.8.0 (64-bit)
# 
# locale:
# [1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] Matrix_1.0-14   lattice_0.20-23 igraph_0.6.6    reshape2_1.2.2  ggplot2_0.9.3.1
# 
# loaded via a namespace (and not attached):
#  [1] colorspace_1.2-4   dichromat_2.0-0    digest_0.6.3       grid_3.0.2         gtable_0.1.2       labeling_0.2      
#  [7] MASS_7.3-29        munsell_0.4.2      plyr_1.8           proto_0.3-10       RColorBrewer_1.0-5 scales_0.2.3      
# [13] stringr_0.6.2      tools_3.0.2       

推荐答案

modularity(graph, split)在您的igraph版本中不支持边缘权重，因此有所不同.在这种情况下，基本上假定所有边缘的权重为1.

modularity(graph, split) does not support edge weights in your version of igraph, hence the difference. Basically all edges are assumed to have weight 1 in this case.

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