  Spin networks, the quantum states of discrete geometry in loop quantum
gravity, are directed graphs whose links are labeled by irreducible
representations of SU(2), or spins. Cosmic strings are 1-dimensional
topological defects carrying distributional curvature in an otherwise flat
spacetime. In this paper we prove that the classical phase space of spin
networks coupled to cosmic strings may obtained as a straightforward
discretization of general relativity in 3+1 spacetime dimensions. We decompose
the continuous spatial geometry into 3-dimensional cells, which are dual to a
spin network graph in a unique and well-defined way. Assuming that the geometry
may only be probed by holonomies (or Wilson loops) located on the spin network,
we truncate the geometry such that the cells become flat and the curvature is
concentrated at the edges of the cells, which we then interpret as a network of
cosmic strings. The discrete phase space thus describes a spin network coupled
to cosmic strings. This work proves that the relation between gravity and spin
networks exists not only at the quantum level, but already at the classical
level. Two appendices provide detailed derivations of the Ashtekar formulation
of gravity as a Yang-Mills theory and the distributional geometry of cosmic
strings in this formulation.
