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SOCNET  August 2008

SOCNET August 2008

Subject:

Re: clustering, modularity, community structure, etc.

From:

James Moody <[log in to unmask]>

Reply-To:

[log in to unmask]

Date:

Fri, 1 Aug 2008 10:56:02 -0400

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text/plain (118 lines)

*****  To join INSNA, visit http://www.insna.org  *****

Hi Folks - 
While "community structure" is the term that seems to dominate in the phys/stat world, 
there's a *long* history of these algorithms in the traditional social science lit under the topic 
of 'cohesive groups'. 

One basic distinction is on deterministic/graph-theory approaches vs. optimization 
approaches.  For the former, work on overlapping clique structures is a good place to start.  
I'm particularly fond of the overlapping & nested nature of node-connectivity for identifying 
cohesion in networks (see Doug White & Harary; Moody & White).  

For optimization routines, FACTIONS in ucinet is easily accessible and works well for smaller 
nets.  Ken Frank has a nice routine that works on optimizing in-group ties (CliqueFinder - now 
also in a 2-mode version), my peer-influence based model (SN 2001) works well for fairly 
large networks (it's very closely related to eigenvector routines, actually.  I've implemented 
two versions in SAS that also add an optimization technique similar to Frank's where nodes 
are juggled across groups to improve fit plus a second-order pass that looks for group-level 
merges/splits.)  For R users, the LatentNet routines from Hancock et. al. employ a statistical 
modeling framework for finding groups in networks.

There's lots of fun to be had inventing new grouping algorithms, of course, but there are 
some fundamental theory issues to attend to as well.  First, it's not clear that all (most?) 
networks admit of a single optimizing partition (for modularity or any other of your favorite 
clustering metrics) -- that is, in many instances the same network can have multiple partitions 
that fit equally well.  Second, while most recent work has focused on mappings that are 
exhaustive and mutually exclusive (every person to a group), there's often good reason to 
assume (a) that some people are not members of any group (this is key to the NEGOPY 
approach - also implemented in my routines.) and (b) that many people belong to multiple 
groups (think cut-points in node-connectivity).   Developmental Psych routines based on 
factor-loadings allow for both options as either low factor loadings or cross-loadings. 

There are also deep questions about the limits of local and global "groups" -- as those sets 
that optimize modularity (say) for the entire network may not map well to the behavior-
reference set for social actors (so, for example, in school networks you can get a very high 
modularity score by simply assigning kids to within-grade, same-sex partitions.  But finding 
meaningful clusters *within* that set is much more challenging, as the density jump from 
within to between is so high.  But kids don't likely pay much attention to the btwn sex/grade 
distinction, focusing on a much more local network.).  Related,, there are issues about fitting 
the observed network to the mental map of actors -- who are likely at least as motivated by 
their perception of the structure as it's instantiation in a set of survey results.  This is the 
continuing contribution of the work on cognitive networks from Krackhardt et. al in 
soc/management to Cairn's and Cairn's classic work on kids nets.

There is, then, lots of fun work to be done on the application and substantive benefits of 
these sorts of routines in real-life social networks too; to help link a graph-theory/optimization 
problem to behavior.  Scott Gest, Kelly Rulison and I took a fairly basic first-crack at some of 
these questions in our JoSS paper, but there's clearly much more work to be done.  Perhaps 
as with centrality -- where it's taken us some time to come up w. a schema for organizing the 
different sorts of measures (thanks Steve B!) -- we need a good schema for understanding 
what sorts of grouping measures matter most for what sorts of network problems....

Peaceful thoughts,
Jim 


On 1 Aug 2008 at 10:25, Mason Alexander Porter wrote:

> *****  To join INSNA, visit http://www.insna.org  *****
> 
> In addition to the references already posted, let me add this recent 
> review article about community detection (which has references to most 
> but not all---in particular not the 08 arxiv papers that have been 
> mentioned---of the references that have come up in this discussion):
> 
>  	http://arxiv.org/abs/0712.2716
> 
> (Community Structure in Graphs by Santo Fortunato, Claudio 
> Castellano)
> 
> By the way, the Newman-Girvan paper that got mentioned has basically been 
> subsumed by subsequent work that does a better job maximizing modularity. 
> I recommend in particular Mark Newman's 2006 PRE paper on maximizing 
> modularity using eigenvector (spectral) methods.  Or if you're going to 
> use the older paper, please use the published version, as there are one or 
> two typos in the arxiv version of that particular paper that can cause 
> some confusion in implementation.  (I know this from personal experience.)
> 
> 
> Also, I am currently writing a survey article on community detection (stat 
> phys and applied math perspective), but it's not ready to be posted in 
> any public place.  If you are interested in my sending you a copy 
> privately, please e-mail me separately from the mailing list.  (I'll of 
> course want your comments, suggestions, etc., as the current draft is in 
> a pretty horrible state.)
> 
> -----
> Mason
> 
> -----------------------------------------------------------------------------
>   Mason A. Porter
>   University Lecturer (and Tutorial Fellow, Somerville College)
>   Oxford Centre for Industrial and Applied Mathematics
>   Mathematical Institute, University of Oxford
> 
>   Homepage: http://www.maths.ox.ac.uk/~porterm, IM: tepid451
>   Blog: http://masonporter.blogspot.com/
> -----------------------------------------------------------------------------
>   "Home is where the internet connection is."
> -----------------------------------------------------------------------------
> 
> _____________________________________________________________________
> SOCNET is a service of INSNA, the professional association for social
> network researchers (http://www.insna.org). To unsubscribe, send
> an email message to [log in to unmask] containing the line
> UNSUBSCRIBE SOCNET in the body of the message.


James Moody
Associate Professor of Sociology
Duke University
http://www.soc.duke.edu/~jmoody77/

_____________________________________________________________________
SOCNET is a service of INSNA, the professional association for social
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