Re: [igraph] igraph-help Digest, Vol 117, Issue 3

[MikeS]

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()
сond <-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
сond <- c(сond, 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(сond)-1), сond, 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