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On Sun, Oct 27, 2013 at 12:21:10PM -0400, Jordi Comas wrote:
>    ***** To join INSNA, visit http://www.insna.org *****
>    Hi-
>    Conceptually, a given node's amount of brokerage as measure by
>    itsconstraint a la Burt's definitions seems the same to me as a clustering
>    coefficient.
>    In other words, for a given node, the constraint may be .5. �For the whole
>    network, those constraint measures could be averaged.
>    A weighted clustering coefficient would measure for each node, how much
>    triadic closure is observed in its one-degree network neighborhood.
>    Thoughts? �If there are differences in measures, is it due to networks
>    perhaps having several components? Or isolates?

Hi Jordi, 

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).

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.

My2Pence

Enzo

-- 
[ Enzo Nicosia - School of Mathematical Sciences - Queen Mary UL ]
[ aka KatolaZ --- GLUG Catania -- Freaknet Medialab -- Poetry -- ]
[ v.nicosia[at]qmul.ac.uk - vincenzo.nicosia [at] ct.infn.it  -- ]
[ katolaz [at] yahoo [dot] it  -- katolaz [at] freaknet.org   -- ]
[ GPG finger:  8E59 D6AA 445E FDB4 A153 3D5A 5F20 B3AE 0B5F 062F ]

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