  We introduce gauge networks as generalizations of spin networks and lattice
gauge fields to almost-commutative manifolds. The configuration space of quiver
representations (modulo equivalence) in the category of finite spectral triples
is studied; gauge networks appear as an orthonormal basis in a corresponding
Hilbert space. We give many examples of gauge networks, also beyond the
well-known spin network examples. We find a Hamiltonian operator on this
Hilbert space, inducing a time evolution on the C*-algebra of gauge network
correspondences.
  Given a representation in the category of spectral triples of a quiver
embedded in a spin manifold, we define a discretized Dirac operator on the
quiver. We compute the spectral action of this Dirac operator on a
four-dimensional lattice, and find that it reduces to the Wilson action for
lattice gauge theories and a Higgs field lattice system. As such, in the
continuum limit it reduces to the Yang-Mills-Higgs system. For the
three-dimensional case, we relate the spectral action functional to the
Kogut-Susskind Hamiltonian.
