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The densities, ρ, speed of sound, u, heat capacities, C p of pure 1-ethyl-3-methylimidazolium tetrafluoroborate, 1-methyl pyrrolidin-2-one, pyrrolidin-2-one, pyridine and ternary mixtures of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + 1-methyl pyrrolidin-2-one or pyrrolidin-2-one (2) + pyridine (3) and their binary mixtures of 1-methyl pyrrolidin-2-one or pyrrolidin-2-one (2) + pyridine (3) have been measured as a function of composition at (293.15, 298.15, 303.15, and 308.15) K and atmospheric pressure. The observed densities and speeds of sound data have been employed to determine excess molar volumes, V E and excess isentropic compressibilities, κS E of the investigated mixtures. The observed thermodynamic properties of the binary as well as ternary mixtures have been calculated by utilizing the topology of the constituents of mixtures (graph theory). It has been observed that graph theory successfully describes well the V E and κS E data of the studied binary and ternary ionic liquid mixtures.