In recent years the development of computational techniques that build models to correctly assign chemical compounds to various classes or to retrieve potential drug-like compounds has been an active area of research. Many of the best-performing techniques for these tasks utilize a descriptor-based representation of the compound that captures various aspects of the underlying molecular graph's topology. In this paper we compare different set of descriptors that are currently used for chemical compound classification. In this process, we also introduce four different descriptors derived from all connected fragments present in the molecular graphs. In addition, we introduce an extension to existing vector-based kernel functions to take into account the length of the fragments present in the descriptors. We experimentally evaluate the performance of the previously introduced and the new descriptors in the context of SVM-based classification and ranked-retrieval on 28 classification and retrieval problems derived from 18 datasets. Our experiments show that for both these tasks, the new descriptors consistently and statistically outperform previously developed schemes based on the widely used fingerprint- and Maces keys-based descriptors, as well as recently introduced descriptors obtained by mining and analyzing the structure of the molecular graphs.