The present invention provides a star-connected network (C1-C4, P1-P8) having a number of peripheral nodes (P1-P8) and a central control arrangement (C1-C4). Each peripheral node has means for restricting communications across the network to the central control arrangement using a respective encrypted connection unless the peripheral node has received explicit authorisation from the control arrangement to set up a direct connection with another peripheral node. The central control arrangement comprises: means for establishing an encrypted connection with each peripheral node; means for exchanging control packets with two or more peripheral nodes using two or more respective encrypted connections in order to set up an authorised connection between two peripheral nodes; a database storing security policy information specifying what connections between peripheral nodes are allowable; and authorisation means for authorising connections which are allowable according to the stored security policy information using the control packet exchanging means.