  In the social sciences, the debate over the structural foundations of social
capital has long vacillated between two positions on the relative benefits
associated with two types of social structures: closed structures, rich in
third-party relationships, and open structures, rich in structural holes and
brokerage opportunities. In this paper, we engage with this debate by focusing
on the measures typically used for formalising the two conceptions of social
capital: clustering and effective size. We show that these two measures are
simply two sides of the same coin, as they can be expressed one in terms of the
other through a simple functional relation. Building on this relation, we then
attempt to reconcile closed and open structures by proposing a new measure,
Simmelian brokerage, that captures opportunities of brokerage between otherwise
disconnected cohesive groups of contacts. Implications of our findings for
research on social capital and complex networks are discussed.
