  Two-dimensional transition metal dichalcogenides represent an emerging class
of materials exhibiting various intriguing properties, and integration of such
materials for potential device applications will necessarily encounter creation
of different boundaries. Using first-principles approaches, here we investigate
the structural, electronic, and magnetic properties along two inequivalent
zigzag M and X edges of MX$_{2}$ (M=Mo, W; X=S, Se). Along the M edges, we
reveal a previously unrecognized but energetically strongly preferred (2x1)
reconstruction pattern, which is universally operative for all the MX$_{2}$,
characterized by a self-passivation mechanism through place exchanges of the
outmost X and M edge atoms. In contrast, the X edges undergo a more moderate
(2x1) or (3x1) reconstruction for MoX$_{2}$ or WX$_{2}$, respectively. We
further use the prototypical zigzag MoX$_{2}$ nanoribbons to demonstrate that
the M and X edges possess distinctly different electronic and magnetic
properties, which are discussed for spintronic and catalytic applications.
