Re: [igraph] igraph-help Digest, Vol 117, Issue 5

[MikeS]

Tamas, thanks you for reply.

>What does get.edgelist(g) return? Does it return the proper edge list
>of the graph?

Yes, get.edgelist(g) returns the proper edge list of the igraph g.

g <- make_graph( ~ A-B-C-D-A, E-A:B:C:D,
                       F-G-H-I-F, J-F:G:H:I,
                       K-L-M-N-K, O-K:L:M:N,
                       P-Q-R-S-P, T-P:Q:R:S,
                       B-F, E-J, C-I, L-T, O-T, M-S,
                       C-P, C-L, I-L, I-P)
>g
IGRAPH UN-- 20 42 --
+ attr: name (v/c)
+ edges (vertex names):
 [1] A--B A--D A--E B--C B--E B--F C--D C--E C--I C--L C--P D--E E--J F--G F--I
[16] F--J G--H G--J H--I H--J I--J I--L I--P K--L K--N K--O L--M L--O L--T M--N
[31] M--O M--S N--O O--T P--Q P--S P--T Q--R Q--T R--S R--T S--T

> get.edgelist(g)
      [,1] [,2]
 [1,] "A"  "B"
 [2,] "A"  "D"
 [3,] "A"  "E"
 [4,] "B"  "C"
 [5,] "B"  "E"
 [6,] "B"  "F"
 [7,] "C"  "D"
 [8,] "C"  "E"
 [9,] "C"  "I"
[10,] "C"  "L"
[11,] "C"  "P"
[12,] "D"  "E"
[13,] "E"  "J"
[14,] "F"  "G"
[15,] "F"  "I"
[16,] "F"  "J"
[17,] "G"  "H"
[18,] "G"  "J"
[19,] "H"  "I"
[20,] "H"  "J"
[21,] "I"  "J"
[22,] "I"  "L"
[23,] "I"  "P"
[24,] "K"  "L"
[25,] "K"  "N"
[26,] "K"  "O"
[27,] "L"  "M"
[28,] "L"  "O"
[29,] "L"  "T"
[30,] "M"  "N"
[31,] "M"  "O"
[32,] "M"  "S"
[33,] "N"  "O"
[34,] "O"  "T"
[35,] "P"  "Q"
[36,] "P"  "S"
[37,] "P"  "T"
[38,] "Q"  "R"
[39,] "Q"  "T"
[40,] "R"  "S"
[41,] "R"  "T"
[42,] "S"  "T"

Mike

2016-04-06 0:39 GMT+07:00 MikeS <address@hidden>:
> Tamas thanks you for the code.
>
> I couldn't find the package sparseMatrix.
> The packages 'plyr', 'Matrix' were installed and uploaded to the R
> Console. Then I have tried to execute your code, but unfortunatly I
> have the error. My vector memb is:
>> memb
> # [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3
>> pairs <- count(matrix(memb[get.edgelist(g)], ncol=2))
> #  x.1 x.2 freq
> # 1  NA  NA   42
>
> The pairs have values 'NA' in the 1st and 2nd column.
>
> Tamas, I have saw that you are not familiar with R.
> Could someone please give idea how to fix this error?
>
> I think that the error connects with the command: memb[get.edgelist(g)], 
> because
>
>> memb[get.edgelist(g)]
> [1] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
> [26] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 
> NA
> [51] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 
> NA
> [76] NA NA NA NA NA NA NA NA NA
>
> Thanks.
> Mike
>
> 2016-04-05 23:00 GMT+07:00  <address@hidden>:
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>> Today's Topics:
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>>    1. Re: igraph-help Digest, Vol 117, Issue 3 (Tamas Nepusz)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Tue, 5 Apr 2016 12:38:50 +0200
>> From: Tamas Nepusz <address@hidden>
>> To: Help for igraph users <address@hidden>
>> Subject: Re: [igraph] igraph-help Digest, Vol 117, Issue 3
>> Message-ID:
>>         <address@hidden>
>> Content-Type: text/plain; charset=UTF-8
>>
>> Intra-cluster and inter-cluster edge counts can be calculated much
>> easier as follows (and maybe there are solutions that are even better
>> - I'm not familiar with R):
>>
>> library(plyr)
>> library(sparseMatrix)
>> pairs <- count(matrix(memb[get.edgelist(g)], ncol=2))
>> pairs <- sparseMatrix(i=pairs$x.1, j=pairs$x.2, x=pairs$freq)
>> pairs <- pairs + t(pairs)
>>
>> Then the intra-cluster edge counts are given by diag(pairs)/2 (note
>> the division by two) and the inter-cluster edge counts between cluster
>> i and j are given by pairs[i, j]. Row and column sums belong to the
>> number of edges incident on a given cluster.
>>
>> T.
>>
>>
>> On Mon, Apr 4, 2016 at 2:11 PM, MikeS <address@hidden> wrote:
>>> Hello,
>>>
>>> Tamas thanks you for reply.
>>>
>>> I have tried to write a script to calculate the conductance in genenal case.
>>> I have used the definition of conductance from the paper
>>> http://cs.stanford.edu/people/jure/pubs/comscore-icdm12.pdf
>>> My code is shown below. I have the error: "in `[.data.frame`(tmp,
>>> c("X1", "X2")) : undefined columns selected" on the line: "long <-
>>> ....."
>>> But code is working. I would like to fix this error and than to test
>>> the code on some dataset.
>>> Could someone please give remarks, comments to the code?
>>>
>>> library(igraph)
>>> g <- make_graph( ~ A-B-C-D-A, E-A:B:C:D,
>>>                       F-G-H-I-F, J-F:G:H:I,
>>>                       K-L-M-N-K, O-K:L:M:N,
>>>                       P-Q-R-S-P, T-P:Q:R:S,
>>>                       B-F, E-J, C-I, L-T, O-T, M-S,
>>>                       C-P, C-L, I-L, I-P)
>>>
>>> comm <- walktrap.community(g)
>>>
>>> mS <- vector() # the number of edges in S
>>> cS <- vector() # the number of edges on the boundary of S
>>> m <- vector()
>>> ?ond <-vector()
>>>
>>> for (s in 0: nrow(comm$merges)) {
>>>     memb <- cutat(comm, steps=s)
>>>     m <- c(m, modularity (g, memb, weights=NULL))
>>>     g2<-make_clusters(g, memb)
>>>
>>> # intra-cluster edges
>>>
>>> mS <- sapply(unique(membership(g2)), function(i) {
>>>     vs<- which(membership(g2)==i)
>>>     subg1<-induced.subgraph(g, vs)
>>>       ecount(subg1)
>>>       })
>>>
>>> # inter-cluster edges
>>>
>>> dcs <- data.frame(combn(unique(membership(g2)), 2))
>>> cS <- sapply(dcs, function(x) {
>>>   es<-E(g)[V(g)[membership(g2)==x[1]] %--% V(g)[membership(g2)==x[2]]]
>>>   length(es)
>>>   })
>>> tmp  <- data.frame(t(dcs[1,]), t(dcs[2,]), cS)
>>> long <- cbind(tmp["cS"], stack(tmp[c("X1","X2")]), row.names = NULL)
>>> # Error in `[.data.frame`(tmp, c("X1", "X2")) : undefined columns selected
>>>
>>> cS <- with( long, tapply(cS, values, sum))
>>>
>>> # Conductance
>>> ?ond <- c(?ond, min(cS/(2*mS + cS)))
>>> }
>>> par(mfrow=c(1:2))
>>> plot(0:(length(m)-1), m, col="blue",xlab="Steps",ylab="Modularity")
>>> plot(0:(length(?ond)-1), ?ond, col="blue",xlab="Steps",ylab="Conductance")
>>>
>>> 2016-04-03 23:01 GMT+07:00  <address@hidden>:
>>>> Hi,
>>>>
>>>> There is no error in your implementation, although the way you define
>>>> conductance is not exactly the way it is usually defined in the graph
>>>> theory literature. (As far as I know, conductance is usually
>>>> calculated for a cut of a graph, i.e. a partitioning into two disjoint
>>>> sets, and the conductance of a graph is simply the minimum conductance
>>>> over all possible cuts). The way you defined conductance is simply the
>>>> ratio of the number of edges between clusters and the number of edges
>>>> within clusters. Now, before the first merge, obviously all the edges
>>>> are between clusters, so you divide a nonzero value with zero, hence
>>>> you get infinity. After having performed all the merges, obviously all
>>>> the edges are within clusters, so you divide zero with a nonzero
>>>> value, getting zero in the end.
>>>>
>>>> So, there's nothing wrong with your code, but the way you defined
>>>> conductance is not suitable for selecting an "optimal" number of
>>>> clusters based on its extrema.
>>>>
>>>> T.
>>>>
>>>>
>>>> On Sat, Apr 2, 2016 at 4:03 AM, MikeS <address@hidden> wrote:
>>>>> Tamas, thanks you for reply.
>>>>> My code does not have syntactical error now.
>>>>> But I concerned about the result, I think I have a logical error.
>>>>>
>>>>> A modularity curve has the maximum value 0.4583 inside the steps'
>>>>> range (on step with no.=18), but conductance curve has extremum 0 on
>>>>> the right boundary.
>>>>>
>>>>>> max(m)
>>>>> [1] 0.4583333 # index =18
>>>>>> max(con)
>>>>> [1] 0 # index = 20
>>>
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