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Context. Inner cavities, accretion arms and density waves are characteristic structures in the density distribution of circumbinary disks. They are the result of the tidal interaction of the non-axisymmetric gravitational forces of the central binary with the surrounding disk and are most prominent in the inner region, where the asymmetry is most pronounced. Aims. The goal of this study is to test the feasibility of reconstructing the gas density distribution and quantifying properties of structures in the inner regions of edge-on circumbinary disks using multiple molecular line observations. Methods. The density distribution in circumbinary disks is calculated with two-dimensional hydrodynamic simulations. Subsequently, molecular line emission maps are generated with 3D radiative transfer simulations. Based on these, we investigate the observability of characteristic circumbinary structures located in the innermost region for spatially resolved and unresolved disks. Results. We find that it is possible to reconstruct the inner cavity, accretion arms and density waves from spatially resolved multi-wavelength molecular line observation of circumbinary disks seen edge-on. For the spatially unresolved observation only an estimate for the density gradient in the transition area from cavity to inner disk rim can be derived.