Re: [R] Social Network Analysis

From: Gabor Csardi <csardi_at_rmki.kfki.hu>
Date: Thu, 24 May 2007 16:43:40 +0200

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)
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 {
```

}
}
}

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},
> }
>
> 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},
> }
>
> > 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@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
> >> 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@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
> and provide commented, minimal, self-contained, reproducible code.

```--
Csardi Gabor <csardi_at_rmki.kfki.hu>    MTA RMKI, ELTE TTK

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