Collective circular motion is a common yet spectacular behaviorofpigeonflocks. Efficient and robust inter-individual communication is required forflockcoordination during this widely-spreaded movement pattern. When aflockhovers near the home loft, the rotational direction undergoes regular spontaneous variations. Based on intensive analysesofhigh spatial-temporal resolution GPS data, we quantified the intensityofvelocity alignment among different individualsintermsoftheir velocity fluctuations. It is found thatpigeonflocks employ an intermittent interaction (alignment) mechanism, where intra-group information transmission is not required at every instant. However, the unionofthe topologiesofseveral consecutive interaction networks always keeps connected. This biological observation strongly suggests the presenceofa jointly connected topologyinpigeonflocks, which helps substantially reduce the communication and/or information processing requirements while retaining the agility and stabilityofthe group. Finally, we conducted extensive investigation on the interaction mechanism as well as the spontaneous changesinrotational directionofpigeonflocks. These results shed some light onto the coordination mechanism explorationofbird flocks' collective motions.