A real-time network-analysis system comprises a network appliance and a plurality of management devices. The network appliance continuously monitors an object network and synthesizes a current network image comprising contemporaneous indicators of connectivity, occupancy, and performance of the object network. A management-client device may gain access to the network image for timely control and for use in producing long-term network-evolution plans. To enable the creation of a real-time network image, optimized topology synthesis algorithms are devised to minimize the computational effort. The real-time network-analysis system is adapted for use with an object network employing a variety of routing protocols, such as link-state protocols, and network-management protocols, such as the Simple-Network-Management protocol.