[Update 2021 - Corrigendum in Geomorphology] Statistical metrics can be used to analyse the morphology of natural or simulated karst systems; they allow describing, comparing, and quantifying their geometry and topology. In this paper, we present and discuss a set of such metrics. We study their properties and their usefulness based on a set of more than 30 karstic networks mapped by speleologists. The data set includes some of the largest explored cave systems in the world and represents a broad range of geological and speleogenetic conditions allowing us to test the proposed metrics, their variability, and their usefulness for the discrimination of different morphologies. All the proposed metrics require that the topographical survey of the caves are first converted to graphs consisting of vertices and edges. This data preprocessing includes several quality check operations and some corrections to ensure that the karst is represented as accurately as possible. The statistical parameters relating to the geometry of the system are then directly computed on the graphs, while the topological parameters are computed on a reduced version of the network focusing only on its structure. Among the tested metrics, we include some that were previously proposed such as tortuosity or the Howard's coefficients. We also investigate the possibility to use new metrics derived from graph theory. In total, 21 metrics are introduced, discussed in detail, and compared on the basis of our data set. This work shows that orientation analysis and, in particular, the entropy of the orientation data can help to detect the existence of inception features. The statistics on branch length are useful to describe the extension of the conduits within the network. Rather surprisingly, the tortuosity does not vary very significantly. It could be heavily influenced by the survey methodology. The degree of interconnectivity of the network, related to the presence of maze patterns, can be measured using different metrics such as the Howard's parameters, global cyclic coefficient, or the average vertex degree. The average vertex degree of the reduced graph proved to be the most useful as it is simple to compute, it discriminates properly the interconnected systems (mazes) from the acyclic ones (tree-like structures), and it permits us to classify the acyclic systems as a function of the total number of branches. This topological information is completed by three parameters, allowing us to refine the description. The correlation of vertex degree is rather simple to obtain. It is systematically negative on all studied data sets indicating a predominance of disassortative networks among karst systems. The average shortest path length is related to the transport efficiency. It is shown to be mainly correlated to the size of the network. Finally, central point dominance allows us to identify the presence of a centralized organization.