1. A fault management apparatus for identifying a cause of fault in a communication network having a communication function in a hierarchical structure of a plurality of layers, comprising: an input device which inputs monitor information specifying a transmitter and a destination as a monitoring target; a generation device which generates communication availability information indicating availability of communication between a plurality of transmitters and a plurality of destinations on each layer before and after a communication state between the transmitter and destination as the monitoring target changes from available to unavailable; a storage device which stores the generated communication availability information; an identification device which identifies an device and a layer as a cause of fault by repeating, layer by layer starting from a search starting layer toward a lower layer, processes of dividing the communication network into a plurality of affected ranges being affected by the fault by comparing the communication availability information before and after the communication state of the monitoring target changes and grouping destinations in paths where the communication state has changed from available to unavailable, and of deducing an interface of a device located at a border between the affected ranges as a fault occurrence point; and an output device which outputs information about the plurality of affected ranges and the fault occurrence point.