[R] Social Network Analysis

[Tom Backer Johnsen]

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/ |
>> +----------------------------------------------------------------+
>>
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> 


-- 
+----------------------------------------------------------------+
| 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/ |
+----------------------------------------------------------------+