  Graphene zigzag nanoribbons, initially in a topologically ordered state,
undergo a topological phase transition into crossover phases distinguished by
quasi-topological order. We computed mutual information for both the
topologically ordered phase and its crossover phases, revealing the following
results: (i) In the topologically ordered phase, A-chirality carbon lines
strongly entangle with B-chirality carbon lines on the opposite side of the
zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii)
The upper zigzag edge entangles with non-edge lines of different chirality on
the opposite side of the ribbon. (iii) Entanglement increases as more carbon
lines are grouped together, regardless of the lines' chirality. No long-range
entanglement was found in the symmetry-protected phase in the absence of
disorder.
