Quantum networks scale the advantages of quantum communication protocols to more than just two distant users. Here we present a fully connected quantum network architecture in which a single entangled photon source distributes quantum states to a multitude of users . Our network architecture thus minimizes the resources required of each user without sacrificing security or functionality. As no adaptations of the source are required to add users, the network can readily be scaled to a large number of clients, whereby no trust in the provider of the quantum source is required. Unlike previous attempts at multi-user networks, which have been based on active components, and thus limited to some duty cycle, our implementation is fully passive and thus provides the potential for unprecedented quantum communication speeds. We experimentally demonstrate the feasibility of our approach using a single source of bi-partite polarization entanglement which is multiplexed into 12 wavelength channels to distribute 6 states between 4 users in a fully connected graph using only 1 fiber and polarization analysis module per user.