  We argue how to identify supersymmetric quiver quantum mechanics description
of BPS states, which arise in string theory in brane systems representing
knots. This leads to a surprising relation between knots and quivers: to a
given knot we associate a quiver, so that various types of knot invariants are
expressed in terms of characteristics of a moduli space of representations of
the corresponding quiver. This statement can be regarded as a novel type of
categorification of knot invariants, and among its various consequences we find
that Labastida-Mari\~no-Ooguri-Vafa (LMOV) invariants of a knot can be
expressed in terms of motivic Donaldson-Thomas invariants of the corresponding
quiver; this proves integrality of LMOV invariants, conjectured originally
based on string theory and M-theory arguments.
