A method of particle characterization by measuring their mobility diameter, d(m), mass, m, and vacuum aerodynamic diameter, d(a)(vac) is proposed and tested for diesel- and flame soot agglomerates having mobility sizes 300-768 nm. The method involves no assumptions other than the knowledge of the particle inherent density. Experiments were performed to establish mass-mobility relationship. The agglomerates' mass-mobility exponent (D-fm) was found to be 2.31 and 1.98 for diesel-soot and flame-soot particles, respectively. The dynamic shape factors (DSFs) of the agglomerates in vacuum and at atmospheric pressure were deduced from the data measured in the range from 2 to 5 for diesel-soot and from 2.7 to 4.3 for flame-soot particles, respectively. The vacuum DSFs are significantly higher than those measured at atmospheric pressure. Independently, from the measured agglomerates' vacuum aerodynamic diameter d(a)(vac) and mass m we evaluated their vacuum mobility diameters, d(m)(vac), and the concomitant vacuum fractal dimension, D-pr, relating m and d(m)(vac): m = k(pr) (d(a)(vac)/d(p))(Dpr) and governing also the agglomerates' projected properties. Despite the clear difference in D-fm, determined from the mass-mobility relationship, both soot particles have close vacuum properties D-pr,D- k(pr), reflecting the screening effect by monomer primary particles, composing the agglomerates. A method is proposed to determine the average primary particle diameter d(p), from the measured agglomerates m - d(a)(vac) power dependence. The model of Vainshtein & Shapiro (2005), for agglomerates' drag in rarefied gases, is used to rationalize and correlate the measured experimental results. We found that the agglomerates' DSFs are very sensitive with respect to their structure, as expressed in their fractal dimension (D-f). Therefore we proposed a method of retrieving the agglomerates' D-f from the DSFs measured in the transition regime, on the basis of an appropriate theoretical model for agglomerates' drag. (C) 2011 Elsevier Ltd. All rights reserved.