This paper proposes a novel clustering method based on graph theory for analysis of biological networks. In this method, each biological network is treated as an undirected graph and edges are weighted based on similarities of nodes. Then, maximal components, which are defined based on edge connectivity, are computed and the nodes are partitioned into clusters by selecting disjoint maximal components. The proposed method was applied to clustering of protein sequences and was compared with conventional clustering methods. The obtained clusters were evaluated using P-values for GO(GeneOntology) terms. The average P-values for the proposed method were better than those for other methods.