The densities, rho, speeds of sound, u of 1-ethyl-3-methylimidazolium tetrafluoroborate (i) + acetone or dimethylsulphoxide (j) binary mixtures at T/K = (293.15, 298.15, 303.15, 308.15) and excess molar enthalpies, H-E of the same mixtures at T/K = (298.15) have been measured over entire mole fraction using DSA-5000 and 2-drop microcalorimeter respectively. The measured data have been utilized to calculate excess molar volumes, V-E and excess isentropic compressibilities, kappa(E)(S). The Graph theory (which deals with topology of the constituents of mixtures) has been applied to calculate (i) state of components of ionic liquid mixtures in their pure and mixed state; (ii) nature and extent of interactions existing in mixtures; and (iii) V-E, H-E and kappa(E)(S) values. Topological investigation of V-E data in terms of Graph theory suggest that while 1-ethyl-3-methylimidazolium tetrafluoroborate is characterized by ionic attraction and exist as monomer; acetone or dimethylsulphoxide exist as associated molecular entities. Further, 1-ethyl-3-methylimidazolium tetrafluoroborate (i) + acetone or dimethylsulphoxide (j) mixtures are characterized by interactions between hydrogen atom of (C-2) of [emim](+) cation with oxygen atom of acetone or dimethylsulphoxide and fluorine atom of [BF4](-) anion with carbon atom of acetone or sulphur atom of dimethylsulphoxide. The IR studies lend additional support to the nature and extend of interactions in the studied mixtures. The V-E, H-E and kappa(E)(S) values calculated by Graph theory compare well with their corresponding experimental values and PFP theory correctly calculate the sign of V-E, H-E and kappa(E)(S) values of the studied mixtures. (C) 2013 Elsevier Ltd. All rights reserved.