  In this paper we propose an algebraic formalization of connectors in the
quantitative setting, in order to address their non-functional features in
architectures of component-based systems. We firstly present a weighted Algebra
of Interactions over a set of ports and a commutative and idempotent semiring,
which is proved sufficient for modeling well-known coordination schemes in the
weighted setup. In turn, we study a weighted Algebra of Connectors over a set
of ports and a commutative and idempotent semiring, which extends the weighted
Algebra of Interactions with types that encode Rendezvous and Broadcast
synchronization. We show the expressiveness of the algebra by modeling the
weighted connectors of several coordination schemes. Moreover, we derive two
subalgebras, namely the weighted Algebra of Synchrons and the weighted Algebra
of Triggers, and study their properties. Finally, we introduce a concept of
congruence relation for connectors in the weighted setup and we provide
conditions for proving such a congruence.
