The clustering problem is one of the main problems which can be encountered in a data analysis. This problem can be modelled by means of a graph; finding clusters means finding cliques in the graph. Often there is a need to find clusters (cliques) in a graph in different ways and to construct a list of clusters. This paper describes two such ways, these can be stated as the cluster minimum covering problem and the vertex cluster minimum partitioning problem. This paper describes new ant algorithms which were used in order to make a list of clusters in both presented problems, and also discusses the results of their comparison.