We present a graph theoretical procedure to generate all the topology-distinct structures for water clusters. The hydrogen bond matrix (H-B matrix) is defined and used to enumerate the topology-distinct structures. The generated hydrogen bond matrices are used as the theoretical framework to obtain all the topology-distinct local minima for (H2O)(n) (n less than or equal to 4); each of the local minima is different in the topology of the hydrogen bonding pattern. (C)2002 Elsevier Science B.V. All rights reserved.