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One of the interesting issues in the management of large computer networks is to partition the network into clusters and then to perform the management for each cluster. This paper presents a basic discussion on the initial clustering problem for a given network. The initial clustering problem C is defined as follows. Given a graphic representation G(V,E), V-n of a network and a set of nodes G-(c)1≤ r ≤ m) &epsive; 1, the graph G is to be partitioned into m connected subgraphs Gi = (Vi, Ei) (1≦i≦m) of G satisfying the following conditions: &o1; V, O C= (c), &o2; V, ≦K (a positive integer); and &o3; the distance between v&epsive; V, and Cx&epsive; C is minimum when x = i. The following results were obtained for the time complexity of the problem C: (1) the initial clustering problem C is in general NP-hard; and (2) the sub-problem obtained by deleting the condition &o2; can be solved in O(n⊃). [ABSTRACT FROM AUTHOR]