1. Haplotype network construction is a widely used approach for analysing and visualising the relationships among DNA sequences within a population or species. This approach has some problems such as how to quantify alternative links among sequences, or how to plot efficiently networks to compare them easily. 2. In this paper, a new method is presented: the randomized minimum spanning tree method, based on randomizing the input order of the data in order to produce alternative branchings in the haplotype network. It is shown that this new method can produce, at least in some situations, networks with less alternative links than the minimum spanning network method. 3. A new graphical display of haplotype networks is introduced here. This is based on calculating the coordinates of the haplotypes from a multidimensional scaling of the haplotype distance matrix. The display can be done in two or three dimensions. The eigenvalues extracted from the multidimensional scaling analysis give an indication of the relevant number of dimensions. 4. These tools are illustrated with the analyses of published data on the leopard and on the jaguar. These analyses show interesting and contrasting patterns between these two species of big cats. 5. All tools are implemented in R and available in the package pegas.