As a combination of novel hardware architecture and novel system architecture for future ultrahigh-density III-V nanodevice LSIs, the authors' group has recently proposed a hexagonal binary decision diagram (BDD) quantum circuit approach where gate-controlled path switching BDD node devices for a single or few electrons are laid out on a hexagonal nanowire network to realize a logic function. In this paper, attempts are made to establish a method to grow highly dense hexagonal nanowire networks for future BDD circuits by selective molecular beam epitaxy (MBE) on (1 1 1)B substrates. The (1 1 1)B orientation is suitable for BDD architecture because of the basic three-fold symmetry of the BDD node device. The growth experiments showed complex evolution of the cross-sectional structures, and it was explained in terms of kinetics determining facet boundaries. Straight arrays of triangular nanowires with 60 nm base width as well as hexagonal arrays of trapezoidal nanowires with a node density of 7.5 x 10(6) cm(-2) were successfully grown with the aid of computer simulation. The result shows feasibility of growing high-density hexagonal networks of GaAs nanowires with precise control of the shape and size. (c) 2006 Elsevier B.V. All rights reserved.