[R] Social Network Analysis

Gabor Csardi csardi at rmki.kfki.hu
Thu May 24 16:43:40 CEST 2007 

Tom, thank you for the detailed answer and sorry for the long delay,
i'm at a conference right now. This sadly means that i have no access to
the papers, it will take more time. 

But in the meanwhile, here's a little program which might be useful,

structural.balance <- function(g) {

  triples <- combn(1:vcount(g)-1, 3)
  good <- bad <- 0
  for (t in 1:ncol(triples)) {
    
    tri <- triples[,t]
    edges <- E(g) [ tri %--% tri ]
    if (length(unique(get.edges(g, edges))) < 3) { next }
    if (prod(E(g)[edges]$sign) > 0) {
      good <- good +1
    } else {
      bad <- bad +1
    }
  }
  c(good, bad)
}

It uses the igraph package, version 0.4 or higher. Basically it
extracts all possible triples from the network and first checks
whether it is connected or not. If it is a connected triple then 
it simply multiples the values of the edges to see whether it is
positive or negative.

Here is a little test with a directed random graph with random
edge values:

g <- erdos.renyi.game(20, p=5/20, directed=TRUE)
E(g)$sign <- sample( c(-1,1), ecount(g), repl=TRUE, prob=c(0.5,0.5))

structural.balance(g)

The code is of course suboptimal, it is brute-force, but if your
networks are small it might be good enough.

Best Regards,
Gabor

On Mon, May 14, 2007 at 11:13:11PM +0200, Tom Backer Johnsen wrote:
> Gabor Csardi wrote:
> > Tom,
> > 
> > check the igraph package. Although structural balance is not implemented,
> > for three or four nodes it might be straightforward to do a quick 
> > implemntation which works for small graphs. 
> 
> I will do so.  My graphs are small, but not very small, having from 8 
> to 11 members (actually military units tested four points in time from 
> their formation as strangers and with the last data collection two 
> months later.
> > 
> > Btw. what is exactly you want to do? List the number of balanced and
> > unbalanced triangles? Ot the triangles themselves? What is a semi-cycle?
> 
> Consider a directed and signed graph having three points (also called 
> vertices) with all possible relations (called lines or arcs) present 
> (which does not have to be the case in empirical situations).  In that 
> case there are six possible semicycles, unique sequences of single 
> lines or arcs between the three points.  The sign of a semicycle is 
> the product of the signs of the arcs, a positive semicycle has none or 
> an even number of negative arcs. (e.g. John dislikes James as well as 
> Peter, but Peter likes James, a balanced triad).
> 
> A structural balance index is the number of positive semicycles over 
> the total number of semicycles.  This concept was introduced by:
> 
> @ARTICLE{Cartwright56,
>    author = {Cartwright, Dorwin and Harary, Frank},
>    title = {Structural Balance: A Generalization of {H}eider's Theory},
>    journal = {Psychological Review},
>    year = {1956},
>    volume = {63},
>    pages = {277-293}
> }
> 
> and:
> 
> @BOOK{Harary65,
>    title = {Structural {M}odels: {A}n {I}ntroduction to the {T}heory 
> of {D}irected {G}raphs},
>    publisher = {John Wiley \& Sons Inc},
>    year = {1965},
>    author = {Harary, Frank and Norman, Robert Z. and Cartwright, Dorwin},
>    keywords = {Graph theory, balance},
>    address={New York}
> }
> 
> to use the BibTex format.  This was a generalization in graph 
> theoretical terms to larger structures involving more than three 
> persons (points, vertices) based on the writings of a social 
> psychologist by the name of Fritz Heider. References:
> 
> @ARTICLE{Heider46,
>    author = {Heider, Fritz},
>    title = {Attitudes and {C}ognitive {O}rganization},
>    journal = {J. of Psychology},
>    year = {1946},
>    volume = {21},
>    pages = {107-112}
> }
> 
> @BOOK{Heider58,
>    title = {The Psychology of Interpersonal Relations},
>    publisher = {Wiley},
>    year = {1958},
>    author = {Heider, Fritz},
>    address = {New York}
> }
> 
> > Could you point me to a good online reference about structureal balance?
> 
> As to more recent and online references I am on quite thin ice.  I 
> know of a a few really trustworthy ones, the problem is simply that 
> parts of the field has been occupied by fringe elements within what is 
> called "sociometry".  One evidently good and recent reference to be 
> used as a point of departure is the following:
> 
> @ARTICLE{Hummon03,
>    author = {Hummon, Norman P. and Doreian, Patrick},
>    title = {Some dynamics of social balance processes: {B}ringing 
> {H}eider back into balance theory},
>    journal = {Social Networks},
>    year = {2003},
>    volume = {25},
>    pages = {17-48}
> }
> 
> I have been in contact with the second author of that article, but he 
> did not have time to respond in full, he was on his way to a social 
> networks conference on Corfu (which I would have attended were it not 
> for family matters which had priority).
> 
> I have a *very* preliminary draft of a paper which you may have if you 
> are interested.
> 
> Tom
> 
> > 
> > Thanks,
> > Gabor
> > 
> > On Sat, May 12, 2007 at 11:44:21PM +0200, Tom Backer Johnsen wrote:
> >> R-Netters:
> >>
> >> for (partial sentimental reasons) I am at the the moment working on 
> >> some old data of mine (actually collected 40 years ago this year for 
> >> my thesis) covering development of of social networks in small groups 
> >> over time.  These data consists of signed and directed graphs.
> >>
> >> Apart from the programs I write myself, I am looking for R functions 
> >> for computing what at that time was called "Structural Balance", 
> >> mainly to check on my own programs, where the results are almost to 
> >> good to be true.  I want to limit myself to cycles (semicycles?) of 
> >> length two and three.
> >>
> >> I am aware of the "network" package as well as the "sna" which do not 
> >> seem to quite cover what I need.  On the other hand, the terminology 
> >> may have changed since I looked into the field 40 years ago.  I am 
> >> also aware of the Pajek program and the corresponding book by Nooy, 
> >> Mrvrar, and Batagelj.
> >>
> >> Any other suggestions or pointers?
> >>
> >> Tom
> >> -- 
> >> +----------------------------------------------------------------+
> >> | Tom Backer Johnsen, Psychometrics Unit,  Faculty of Psychology |
> >> | University of Bergen, Christies gt. 12, N-5015 Bergen,  NORWAY |
> >> | Tel : +47-5558-9185                        Fax : +47-5558-9879 |
> >> | Email : backer at psych.uib.no    URL : http://www.galton.uib.no/ |
> >> +----------------------------------------------------------------+
> >>
> >> ______________________________________________
> >> R-help at stat.math.ethz.ch mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> > 
> 
> 
> -- 
> +----------------------------------------------------------------+
> | Tom Backer Johnsen, Psychometrics Unit,  Faculty of Psychology |
> | University of Bergen, Christies gt. 12, N-5015 Bergen,  NORWAY |
> | Tel : +47-5558-9185                        Fax : +47-5558-9879 |
> | Email : backer at psych.uib.no    URL : http://www.galton.uib.no/ |
> +----------------------------------------------------------------+
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Csardi Gabor <csardi at rmki.kfki.hu>    MTA RMKI, ELTE TTK

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