We investigate the effect of supersymmetry preserving mass deformation near the UV fixed point represented by the ${cal N}=6$ ABJM theory. In the context of the gauge/gravity duality, we analytically calculate the leading small mass effect on the renormalized entanglement entropy (REE) for the most general Lin-Lunin-Maldacena (LLM) geometries in the cases of the strip and disk shaped entangling surfaces. Our result shows that the properties of the REE in (2+1)-dimensions are consistent with those of the $c$-function in (1+1)-dimensions. We also discuss the validity of our computations in terms of the curvature behavior of the LLM geometry in the large $N$ limit and the relation between the correlation length and the mass parameter for a special LLM solution.
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