  We follow up on previous work which found that commonly used graph evolution
moves lead to conserved quantities that can be expressed in terms of the
braiding of the graph in its embedding space. We study non-embedded graphs
under three distinct sets of dynamical rules and find non-trivial conserved
quantities that can be expressed in terms of topological defects in the dual
geometry. For graphs dual to 2-dimensional simplicial complexes we identify all
the conserved quantities of the evolution. We also indicate expected results
for graphs dual to 3-dimensional simplicial complexes.
