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.