We present a method for automatically extracting groups of orthologous genes from a large set of genomes by a new clustering algorithm on a weighted multipartite graph. The method assigns a score to an arbitrary subset of genes from multiple genomes to assess the orthologous relationships between genes in the subset. This score is computed using sequence similarities between the member genes and the phylogenetic relationship between the corresponding genomes. An ortholog cluster is found as the subset with the highest score, so ortholog clustering is formulated as a combinatorial optimization problem. The algorithm for finding an ortholog cluster runs in time O(absolute value(E) + absolute value(V) log absolute value(V)), where V and E are the sets of vertices and edges, respectively, in the graph. However, if we discretize the similarity scores into a constant number of bins, the runtime improves to O(absolute value(E) + absolute value(V)). The proposed method was applied to seven complete eukaryote genomes on which the manually curated database of eukaryotic ortholog clusters, KOG, is constructed. A comparison of our results with the manually curated ortholog clusters shows that our clusters are well correlated with the existing clusters.