Primacy analysis in the system of Bulgarian cities

The concept of "primacy" as introduced by Jefferson in 1939 in urban geography leads to the notion of "dominant city" also known as the primate city. Practically, the notion was extended by Sheppard in view of discussing some "hierarchy". The type of dominance is not universal nor any hierarchy reversal. Both can be time and sample dependent. Thus, as an example taking into consideration the existence of both pieces of the puzzle, we consider and discuss the Bulgarian urban system. It is also interesting to compare data on two groups of cities in different time intervals: (i) the whole Bulgaria city system which contains about 250 cities, - studied in the time interval between 2004 and 2011, and (ii) a system of 33 cities, - studied over the time interval 1887 till 2010. These latter cities are selected because the population was already over 10 000 inhabitants in 1946. It is shown that new additional indices are interestingly introduced in order to compensate defects in the Sheppard index. Numerical illustrations are illuminated through a "length ratio" measure, which allows to distinguish the (often) observed departures from the hyperbolic ranking seen by Jefferson.