On the relationship between social cohesion and structural holes

In a continuing series “Highlights of SOCNET” I offer you Vincenzo Nicosia’s email summarizing his cool recently published work: 

In a recent work appeared in Journal of Statistical Physics:
V. Latora, V. Nicosia, P. Panzarasa “Social cohesion, structural
holes, and a tale of two measures”, J. Stat. Phys. 151 (3-4), 745
(2013). (Arxiv version)

We have proved that node degree (k_i), effective size (S_i) and
clustering (C_i) are indeed connected by the simple functional
relation:

S_i = k_i – (k_i – 1)C_i

This means that effective size and clustering indeed provide similar
information (even if not exactly the same kind of information), and
they should not be used together in multivariate regression models,
since they tend to be collinear.

In that paper we also build on this relationship to define a measure
of Simmelian brokerage, aiming at quantifying the extent to which a
node acts as a broker among two or more cohesive groups which would
otherwise be disconnected.

Which R packages are good for what social network analysis?

Newbies to social network analysis in R should check out this great concise description from Michal Bojanowski on the SOCNET email list.  He writes:

There are two main R packages that provide facilities to store,manipulate and visualize network data. These are “network” and’igraph”. Technically speaking each package provides a specializedclass of R data objects for storing network data plus additionalfunctions to manipulate and visualize them. Each package has itsrelative strengths and weaknesses, but by and large you can do mostbasic network data operations and visualizations in both packagesequally easily. Moreover, you can convert network data objects from”network” to “igraph” or vice versa with functions from the”intergraph” package.Calculating basic network statistics (degree, centrality, etc.) ispossible for both types of objects. For “igraph” objects, functionsfor these purposes are contained in “igraph” itself. For “network”objects, most of the classical SNA routines are contained in the “sna”package.Community detection algorithms (e.g. Newman-Girvan) are available onlyin the “igraph” package.”Fancier things”, especially statistical models for networks (ERGMsetc.) are available in various packages that were build around the”network” package and jointly constitute the ‘statnet’ suite(http://www.statnet.org/). There is also “tnet” package with some moreroutines for among other things two-mode networks, which borrows fromboth “network” and “igraph” world. And of course there is RSiena forestimating actor-oriented models of network dynamics which is notrelated either “network” or “igraph”.As for matrix algebra, it is obviously available within R itself.My recommendation would be to have a look at both “igraph” and”network” and pick the one which seems easier to you as far asmanipulating and visualizing networks is concerned. Have a look at thedocumentation of these packages (e.g. onhttp://www.rdocumentation.org/) and at tutorials on e.g.:- statnet website (http://www.statnet.org/)- igraph homepage (http://igraph.sourceforge.net/)- R labs by McFarland et al (http://sna.stanford.edu/rlabs.php)- Slides and scripts to my Sunbelt workshop(http://www.bojanorama.pl/snar:start)It does not really matter whether you pick “igraph” or “network” asyou can aways convert your network to the other class with ‘asIgraph’or ‘asNetwork’ functions from “intergraph” package and take advantageof the functions available in the “other world”.

Check out more of Michal’s helpful contributions at his blog: http://bc.bojanorama.pl/