Clustering scientific publications in an important problem in bibliometric research. We demonstrate how two software tools, CitNetExplorer and VOSviewer, can be used to cluster publications and to analyze the resulting clustering solutions. CitNetExplorer is used to cluster a large set of publications in the field of astronomy and astrophysics. The publications are clustered based on direct citation relations. CitNetExplorer and VOSviewer are used together to analyze the resulting clustering solutions. Both tools use visualizations to support the analysis of the clustering solutions, with CitNetExplorer focusing on the analysis at the level of individual publications and VOSviewer focusing on the analysis at an aggregate level. The demonstration provided in this paper shows how a clustering of publications can be created and analyzed using freely available software tools. Using the approach presented in this paper, bibliometricians are able to carry out sophisticated cluster analyses without the need to have a deep knowledge of clustering techniques and without requiring advanced computer skills.