This paper addresses a distributed formation control problem of multiple mobile agents using relative positions and local bearings. First, a formation control method via distributed pattern matching is proposed, which is executed over each clique (i.e., complete induced subgraph) of a network. It is shown that this method achieves the best control performance for a given desired formation and network topology in the following sense: The closest formation to the desired one is achieved among all formations achievable by distributed and relative control over the network. Next, a necessary and sufficient network condition is derived under which the desired formation can be obtained. It turns out that a new concept of connectivity, called clique rigidity, plays a crucial role. Finally, the effectiveness of the proposed method is illustrated through simulations in both two and three dimensional spaces.