Abstract: Aiming at the problem of closed loop in the graph theory,we put forward the concept of minimum closed loop and minimum double closed loop,on which nodes satisfy certain properties.Then we put forward the concept of “sunflower” double closed loop,which put forward the formal definition,algorithm and algorithm analysis of the minimum closed loop,minimum double closed loop and “sunflower” double closed loop,which supplement the graph theory about the content of the closed loop.The application of closed loop detection in video is also studied,which provides theory and technology support for the police to detect and quickly lock the criminal suspect in the case of video surveillance.

Key words: Graph,Minimum closed loop,Minimum double closed loop,“Sunflower” double loop