The collective behavior of multi-agent systems is an important studying point for theinvestigation of complex systems, and a basic model of multi-agent systems is the socalled Vicsek model, which possesses some key features of complex systems, suchas dynamic behavior, local interaction, changing neighborhood, etc. This modellooks simple, but the nonlinearly coupled relationship makes the theoretical analysisquite complicated. Jadbabaie et al. analyzed the linearized heading equations inthis model and showed that all agents will synchronize eventually, provided that theneighbor graphs associated with the agents’ positions satisfy a certain connectivitycondition. Much subsequent research effort has been devoted to the analysis of theVicsek model since the publication of Jadbabaie’s work. However, an unresolvedkey problem is when such a connectivity is satisfied. This paper given a sufficientcondition to guarantee the synchronization of the Vicsek model, which is imposedon the model parameters only. Moreover, some counterexamples are given to showthat the connectivity of the neighbor graphs is not sufficient for synchronization ofthe Vicsek model if the initial headings are allowed to be in [0, 2π), which revealssome fundamental differences between the Vicsek model and its linearized version. The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the socalled Vicsek model, which possesses some key features of complex systems, suchas dynamic behavior, local interaction, changing neighborhood, etc. This modellooks simple, but the nonlinearly coupled relationship makes the theoretical analysisquite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that theighborhood relationships associated with the agents’ positions Much subsequent research effort has been devoted to the analysis of theVicsek model since the publication of Jadbabaie’s work. However, an unresolvedkey problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposedon the model p arameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0, 2π), which revealssome fundamental differences between the Vicsek model and its linearized version.