In this paper, molecular topology was used to develop a mathematical model capable of classifying compounds according to their antibacterial activity. Topological indices were used as structural descriptors and their relation to antibacterial activity was determined by applying linear discriminant analysis (LDA) on a group of quinolones, widely used nowadays because of their broad spectrum of activity, well tolerance profile and advantageous pharmacokinetic properties. The topological model of activity obtained included two discriminant functions, selected by a combination of various statistical paremeters such as Fisher-Snedecor F and Wilk's lambda, and allows the reliable prediction of antibacterial activity in any organic compound. After a virtual pharmacological screening on a library of 6375 compounds, the model has selected 263 as active compounds, from which 40% have proven antibacterial activity. The results obtained clearly reveal the high efficiency of molecular topology for the prediction of pharmacological activities. These models are very helpful in the discovery of new applications of natural and synthetic molecules with different chemical or biological properties. Therefore, we finally present 158 strong candidates to be developed as novel antibacterials.