The real-time outage identification and localization of a potentially large number of transmission line outages is of vital importance while fairly challenging under limited measurement resources. To address this issue, an adaptive distributed graph model (ADGM) is innovatively proposed for multiple-line outage identification to hedge limited measurement and noise in the large-scale power system. By integrating a novel Laplacian convolution (LC) operation, the proposed ADGM is forceful in capturing the non-Euclidian structure of nodal voltage phase angle measurement to tackle the real-time outage identification problem effectively with measurement noise. On top of this, a novel breadth walk (BW) operation is proposed to exclude redundant measurement so that enhanced outage identification accuracy can be achieved under measurement lost. BW is then incorporated with LC to release the ADGM from numerous parameters' training burden to achieve the large-scale system outage identification. Numerical simulations are carried out based on the IEEE 30/118/300-node and Polish 2383-node testing systems, which verify the effectiveness, efficiency, and robustness of the proposed model.