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Re: [igraph] about triangle transitivity

 From: Gábor Csárdi Subject: Re: [igraph] about triangle transitivity Date: Fri, 13 Jan 2012 09:04:53 -0500

```Looks good to me.

G.

On Fri, Jan 13, 2012 at 8:18 AM, gunce orman <address@hidden> wrote:
> Ok thank you, Is this code correct for square transitivity counting?
>
> # plot all motifs for 4 nodes (undirected)
> for(i in 0:10)
> { cat("printing motif #",i,"\n")
> pdf(file=paste("c:/",i,".pdf",sep=""),bg="white")
> plot(graph.isocreate(size=4,number=i,directed=FALSE))
> dev.off()
> }
>
> square.transitivity <- function(g)
> { motifs.counts <- graph.motifs(graph=g,size=4)
> # 6: incomplete square (when index starts from 0)
> incomplete.squares <- motifs.counts[7]
> # 8: complete square (when index starts from 0)
> complete.squares <- motifs.counts[9]
> # process 'square'-transitivity
> result <- complete.squares / (complete.squares + incomplete.squares)
> return(result)
> }
>
> # examples
> g <- graph(edges=c(0,1,1,2,2,3,3,0,0,4),directed=FALSE)
> plot(g)
> square.transitivity(g) # supposed to be 1/3 (2 incomplete and 1 complete
> squares)
> g <- barabasi.game(n=100,m=3,directed=FALSE)
> square.transitivity(g)
>
>
> On Thu, Jan 12, 2012 at 3:28 PM, Moses Boudourides
>>
>> Right.
>>
>> --M
>>
>> On Thu, Jan 12, 2012 at 4:26 PM, Gábor Csárdi <address@hidden> wrote:
>> > Yes, although matrix multiplications are expensive. The initial matrix
>> > is probably sparse, so that is fine, but then it gets denser (quickly
>> > if the network is small-world). So this would work only for small
>> > graphs.
>> >
>> > G.
>> >
>> > On Thu, Jan 12, 2012 at 9:23 AM, Moses Boudourides
>> > <address@hidden> wrote:
>> >> Well, another option would be to use the formulas for the powers of
>> >> the adjacency matrix, although it might involve some work to derive
>> >> the corresponding expressions for 5-cycles and higher. I'm not sure,
>> >> this might have been already done in graph theory. If I was attempting
>> >> to do it, I would start from counting redundancies as in the
>> >> fundamental paper of Harary & Ross (Psychometrica, 1952).
>> >>
>> >> --Moses
>> >>
>> >> On Thu, Jan 12, 2012 at 4:00 PM, Gábor Csárdi <address@hidden>
>> >> wrote:
>> >>> Hi,
>> >>>
>> >>> graph.motifs() (in R) supports motifs of size 3 and 4 currently. There
>> >>> is not much more code needed to support larger motifs, but these are
>> >>> not implemented yet.
>> >>>
>> >>> If you are looking for a specific motif, then you can also use the
>> >>> graph.count.subisomorphisms.vf2() function.
>> >>>
>> >>> G.
>> >>>
>> >>> On Thu, Jan 12, 2012 at 4:53 AM, gunce orman <address@hidden>
>> >>> wrote:
>> >>>> Hello,
>> >>>>
>> >>>> Transitivity only measures the number of triangles in a network.  But
>> >>>> there
>> >>>> are other short cycles (e.g., 4-cycles) which are common in networks.
>> >>>> Are we
>> >>>> able to calculate those types of 4- and more cycles as well as
>> >>>> counting
>> >>>> triangles in igraph.
>> >>>>
>> >>>> Thank you
>> >>>>
>> >>>> _______________________________________________
>> >>>> igraph-help mailing list
>> >>>> https://lists.nongnu.org/mailman/listinfo/igraph-help
>> >>>>
>> >>>
>> >>>
>> >>>
>> >>> --
>> >>> Gabor Csardi <address@hidden>     MTA KFKI RMKI
>> >>>
>> >>> _______________________________________________
>> >>> igraph-help mailing list
>> >>> https://lists.nongnu.org/mailman/listinfo/igraph-help
>> >>
>> >> _______________________________________________
>> >> igraph-help mailing list
>> >> https://lists.nongnu.org/mailman/listinfo/igraph-help
>> >
>> >
>> >
>> > --
>> > Gabor Csardi <address@hidden>     MTA KFKI RMKI
>> >
>> > _______________________________________________
>> > igraph-help mailing list
>> > https://lists.nongnu.org/mailman/listinfo/igraph-help
>>
>> _______________________________________________
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>
>
>
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--
Gabor Csardi <address@hidden>     MTA KFKI RMKI

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