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This paper explores the relationship between the inner economical structureof communities and their population distribution through a rank-rank analysisof official data, along statistical physics ideas within two techniques. Thedata is taken on Italian cities. The analysis is performed both at a global(national) and at a more local (regional) level in order to distinguish "macro"and "micro" aspects. First, the rank-size rule is found not to be a standardpower law, as in many other studies, but a doubly decreasing power law. Next,the Kendall and the Spearman rank correlation coefficients which measure pairconcordance and the correlation between fluctuations in two rankings,respectively, - as a correlation function does in thermodynamics, arecalculated for finding rank correlation (if any) between demography and wealth.Results show non only global disparities for the whole (country) set, but also(regional) disparities, when comparing the number of cities in regions, thenumber of inhabitants in cities and that in regions, as well as when comparingthe aggregated tax income of the cities and that of regions. Different outliersare pointed out and justified. Interestingly, two classes of cities in thecountry and two classes of regions in the country are found. "Common sense"social, political, and economic considerations sustain the findings. Moreimportantly, the methods show that they allow to distinguish communities, veryclearly, when specific criteria are numerically sound. A specific modeling forthe findings is presented, i.e. for the doubly decreasing power law and the twophase system, based on statistics theory, e.g., urn filling. The model ideascan be expected to hold when similar rank relationship features are observed infields. It is emphasized that the analysis makes more sense than one through aPearson value-value correlation analysis.

Cross Ranking of Cities and Regions: Population vs. Income