A graph model is often used to represent complex relational information in data clustering. Although there have been several kinds of graph structures, many graph-based clustering methods use a sparse graph model. The structure and weight information of a sparse graph decide the clustering result. This paper introduces a set of parameters to describe the structure and weight properties of a sparse graph. A set of measurement criteria of clustering results is presented based on the parameters. The criteria can be extended to represent the user's requirements. Based on the criteria the paper proposes a customizable algorithm that can produce clustering results according to users' inputs. The preliminary experiments on the customizability show encouraging results.
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