1. An apparatus for monitoring a network in which a label switched path (LSP) is set up, the network including a plurality of routers, comprising: a communication unit that communicates with a router among the plurality of routers; a collection unit that collects LSP path information via the communication unit independently of packet forwarding that uses the LSP, the LSP path information being maintained by the router and including information to be referred to for forwarding a packet by the router and other information exchanged via a message for setting up or maintaining the LSP by the router; a storing unit that stores state information based on the LSP path information collected by the collection unit, the state information including information for identifying an LSP and information on a current path of the LSP; and a display unit that reads the state information for a selected LSP stored by the storing unit and graphically displays how a path of the selected LSP is formed on a corresponding network topology, in accordance with a user's instruction.