Measuring the similarity of charts in graphical statistics

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.

Fractal dimension complexity of gravitation fractals in central place theory

Settlement centers of various types, including cities, produce basins of attraction whose shape can be regular or complexly irregular (from the point of view of geometry). This complexity depends in part on properties of the space surrounding a settlement. This paper demonstrates that by introducing a dynamic approach to space and by including an equation of motion and space resistance, a dramatic change in the stylized static CPT (Central Place Theory) image occurs. As a result of the interplay of gravitational forces, basins of attraction arise around cities, whose boundaries appear to be fractals. This study provides a wealth of spatial fractal complex images which may change the traditional understanding of CPT.