MSE vs topology for GMRFs

Closed form expressions for the MSE for stylized topologies such as complete graph, star and cycle seem very doable.. and so are the error exponents

Chain graph - Full graph -MSE

Hmm.. time to ponder. MSE is not playing nice as a metric. Need to head back to the drawing board. The difference in MSE seen when the topology is switched from full network (complete graph) to chain should be atleast a paradigm shift.
Darn!!