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.

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