Compact graph based representation of complex data can be used for clustering and visualisation. In this chapter we introduce basic concepts of graph theory and present approaches which may generate graphs from data. Computational complexity of clustering and visualisation algorithms can be reduced replacing original objects with their representative elements (code vectors or fingerprints) by vector quantisation. We introduce widespread vector quantisation methods, the k -means and the neural gas algorithms. Topology representing networks obtained by the modification of neural gas algorithm create graphs useful for the low-dimensional visualisation of data set. In this chapter the basic algorithm of the topology representing networks and its variants (Dynamic Topology Representing Network and Weighted Incremental Neural Network) are presented in details.