This brief investigates distributed coordination control problems under a state-dependent communication graph with several inherent links. In the network, an interaction arises between two agents if either their states differ by less than a fixed range or an inherent communication link exists between them. By considering that each agent has a state-dependent control gain, a nonlinear consensus protocol is proposed for single-integrator modeled multi-agent systems. With the validity of some initial condition, the communication graph is shown to be connected at any time, which guarantees asymptotic consensus. It is further shown that this result can apply to the opinion consensus problem. This brief also provides a novel approach to finite-time coordination protocols synthesis. By simply multiplying a time-varying gain, any coordination protocol can be transformed into a finite-time protocol. A simulation example is presented to illustrate the effectiveness of the theoretical result.