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Fault tolerance is one of the important ways to measure the reliability of multiprocessor interconnection networks.g-restricted edge connectivity and g-restricted connectivity can ensure every remaining component is disconnected ,the number of neighbors of vertex is no less than g,which can measure the fault tolerance and reliability of multiprocessor and multichannel system more accurately.Balanced hypercubes is a variant of the hypercube,which has some specific topological properties,it can better meet the needs of the multiprocessor system and many new networks.The {1,2}-restricted edge connectivity and the {1,2}-restricted connectivity of balanced hypercubes were proposed,which could enrich the evaluation system of network fault tolerance and reliability in balanced hypercubes topology and it laid a good foundation for the fault diagnosis algorithm of balances hypercube.