  In a recent work we introduced a measure of importance for groups of vertices
in a complex network. This centrality for groups is always between 0 and 1 and
induces the eigenvector centrality over vertices. Furthermore, its value over
any group is the fraction of all network flows intercepted by this group. Here
we provide the rigorous mathematical constructions underpinning these results
via a semi-commutative extension of a number theoretic sieve. We then
established further relations between the eigenvector centrality and the
centrality proposed here, showing that the latter is a proper extension of the
former to groups of nodes. We finish by comparing the centrality proposed here
with the notion of group-centrality introduced by Everett and Borgatti on two
real-world networks: the Wolfe's dataset and the protein-protein interaction
network of the yeast \textit{Saccharomyces cerevisiae}. In this latter case, we
demonstrate that the centrality is able to distinguish protein complexes.
