Connectors for linear members of wall structure which allows a variety of guide rails, fences, and pipes to be assembled in a desired pattern conveniently are provided. The connector includes a central body of annular shape; at least one socket member 6, the one end of the socket member being connected to the central body and the other end being connected to the linear member, such as pipe, wire or bar; and a rail means that connects the central body and the socket member such that the socket member can be moved along the circumferential surface of the central body.