A data compressor of the present invention comprises: separating means for separating input data having a plurality of vertices with their respective types and values, and reference information between the vertices, into cross reference data with the reference information between the vertices, and a vertex group consisting of the plurality of vertices with the types and values, and for outputting data of the vertex group thus separated; template storing means for storing reference information between vertices having a specific pattern, as a template, wherein the template can share the reference information between the vertices, with other stored templates; template match detecting means for detecting a portion matching the template stored in the template storing means, from the cross reference data separated by the separating means; and template replacing means for replacing the match portion detected by the template match detecting means, in the cross reference data separated by the separating means, with the temperate, in a state in which the reference information between the vertices can be referred to, and for outputting the replaced cross reference data.