We provide an algebraic formalisation of connectors in BIP. These are used to structure interactions in a component-based system. A connector relates a set of typed ports. Types are used to describe different modes of synchronisation: rendezvous and broadcast, in particular. Connectors on a set of ports P are modelled as terms of the algebra AC(P), generated from P by using an binary fusion operator and a unary typing operator. Typing associates with terms (ports or connectors) synchronisation types -- trigger or synchron -- that determine modes of synchronisation. Broadcast interactions are initiated by triggers. Rendezvous is a maximal interaction of a connector including only synchrons. The semantics of AC(P) associates with a connector the set of its interactions. It induces on connectors an equivalence relation which is not a congruence as it is not stable for fusion. We provide a number of properties of AC(P) used to symbolically simplify and handle connectors. We provide examples illustrating applications of AC(P), including a general component model encompassing synchrony, methods for incremental model decomposition, and efficient implementation by using symbolic techniques.