The flexing of the ligaments at the edge of a finite hexagonal honeycomb array is studied using analytical and numerical methods. It is shown that when compressed axially, the ligaments on the border of a hexagonal honeycomb array bend outwardly in contrast to the interior ligaments that bend to a negligible extent, if at all. This boundary effect reduces the overall auxeticity of re-entrant hexagonal honeycombs. Analytical expressions that account for the edge effects on the Poisson's ratio and Young's modulus are obtained using Castigliano's second theorem. These are then tested against numerical simulations showing good agreement at least for the values of the parameters used. Additional investigations indicate that the use of a larger ligament thickness for the ligaments residing on the border of the system mitigates this edge effect on the Poisson's ratio.