We investigate the relation between characteristics of coronal mass ejections and parameterizations of the eruptive capability of solar active regions widely used in solar flare prediction schemes. These parameters, some of which are explored for the first time, are properties related to topological features, namely, magnetic polarity inversion lines (MPILs) that indicate large amounts of stored non-potential (i.e. free) magnetic energy. We utilize the Space Weather Database of Notifications, Knowledge, Information (DONKI) and the Large Angle and Spectrometric Coronograph (LASCO) databases to find flare-associated coronal mass ejections and their kinematic characteristics while properties of MPILs are extracted from Helioseismic and Magnetic Imager (HMI) vector magnetic-field observations of active regions to extract the properties of source-region MPILs. The correlation between all properties and the characteristics of CMEs ranges from moderate to very strong. More significant correlations hold particularly for fast CMEs, which are most important in terms of adverse space-weather manifestations. Non-neutralized currents and the length of the main MPIL exhibit significantly stronger correlations than the rest of the properties. This finding supports a causal relationship between coronal mass ejections and non-neutralized electric currents in highly sheared, conspicuous MPILs. In addition, non-neutralized currents and MPIL length carry distinct, independent information as to the eruptive potential of active regions. The combined total amount of non-neutralized electric currents and the length of the main polarity inversion line, therefore, reflect more efficiently than other parameters the eruptive capacity of solar active regions and the CME kinematic characteristics stemming from these regions.