In terms of the characteristic topology parameters of climate complex networks,the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described.Results of node degrees for the Northern Hemisphere (NH) mid-high latitude (30°N-90°N) circulation system (NHS) networks with and without the Arctic Oscillations (AO),the North Atlantic Oscillations (NAO) and the Pacific-North American pattern (PNA) demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks,thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS.The impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important.The PNA is a relatively independent teleconnection,and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system (TRS).As to the Southern Hemisphere mid-high latitude (30°S-90°S) circulation system (SHS),the impact of the Antarctic Arctic Oscillations (AAO) on the structural stability of the system is most important.In addition,there might be a stable correlation dipole (AACD) in the SHS,which also has important influence on the structure of the SHS networks. In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described. Results of node degrees for the Northern Hemisphere (NH) mid-high latitude (30 ° N-90 ° N) networks with and without the Arctic Oscillations (AO), the North Atlantic Oscillations (NAO) and the Pacific-North American pattern (PNA) demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks, thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS. the impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important. The PNA is a relatively independent teleconnection, and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system (TRS) .A s to the Southern Hemisphere mid-high latitude (30 ° S-90 ° S) circulation system (SHS), the impact of the Antarctic Arctic Oscillations (AAO) on the structural stability of the system is most important. In addition, there might be a stable correlation dipole (AACD) in the SHS, which also has important influence on the structure of the SHS networks.