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Abstract Figures used in statistics and other sciences play a vital role in understanding and analyzing the problems under study. Due to the complexity and diversity of these problems, figures such as cartograms, choropleth maps, or radar charts take various geometric forms. Their visual evaluation from the view of geometric similarity is essential but insufficient. This paper proposes and theoretically justifies new metrics based on graph theory. They make it possible to quickly determine the degree of similarity of the statistical figures used in the research procedure. The new metrics were used to 1. Determine the similarity of the domestic route networks of major U.S. airlines, 2. Determine the similarity of the distribution of votes cast in U.S. presidential election in each state in 2016 and 2020, 3. Compare radar charts of some countries, constructed based on the Global Competitiveness Index, 4. Analyze the similarity of neutrosophic double line graphs representing sets of approximate (neutrosophic) numbers. This improves analytical capabilities concerning various processes mapped with well-known types of statistical charts, such as choropleth maps, radar charts, etc.