  We present the construction of a new family of coherent states for quantum
theories of connections obtained following the polymer quantization. The
realization of these coherent states is based on the notion of graph change, in
particular the one induced by the quantum dynamics in Yang-Mills and gravity
quantum theories. Using a Fock-like canonical structure that we introduce, we
derive the new coherent states that we call the graph coherent states. These
states take the form of an infinite superposition of basis network states with
different graphs. We further discuss the properties of such states and certain
extensions of the proposed construction.
