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For the complex dynamical network (CDN) with uncertainties, this paper defines the links synchronization and synthesizes the adaptive control scheme to realize it. Generally speaking, a CDN can be considered as the composition system with the two coupled dynamic subsystems: the nodes subsystem (NS) and the links subsystem (LS). We observed that there are many results in the existing literature on the NS synchronization, which implies that the state at each node tends to be the same when the NS synchronization happens. However, the LS synchronization is rarely discussed in the existing literature due to its unknown meaning and engineering practice background. Inspired by the ego-networks, this paper employs the time-varying outgoing links at each node to geometrically describe the changing of network topologic structure and regards the values-weighted of outgoing links as the state variables of LS, by which the LS synchronization is introduced, the corresponding control scheme for its implementation is synthesized under the condition that the state of NS is available and the state of LS is unavailable. The control scheme includes the adaptive controller for NS and the coupling strategy for LS. Finally, the effectiveness of proposed control scheme in this paper is verified by a numerical example. [ABSTRACT FROM AUTHOR]