We explore radio and spectroscopic properties of a sample of 14 miniature radio galaxies, i.e. early-type core galaxies hosting radio-loud AGN of extremely low radio power, 10^(27-29) erg s^(-1) Hz^(-1) at 1.4 GHz. Miniature radio galaxies smoothly extend the relationships found for the more powerful FRI radio galaxies between emission line, optical and radio nuclear luminosities to lower levels. However, they have a deficit of a factor of ~100 in extended radio emission with respect to that of the classical example of 3CR/FRI. This is not due to their low luminosity, since we found radio galaxies of higher radio core power, similar to those of 3CR/FRI, showing the same behavior, i.e. lacking significant extended radio emission. Such sources form the bulk of the population of radio-loud AGN in the Sloan Digital Sky Survey. At a given level of nuclear emission, one can find radio sources with an extremely wide range, a factor of >~100, of radio power. We argue that the prevalence of sources with luminous extended radio structures in flux limited samples is due to a selection bias, since the inclusion of such objects is highly favored. The most studied catalogues of radio galaxies are thus composed by the minority of radio-loud AGN that meet the physical conditions required to form extended radio sources, while the bulk of the population is virtually unexplored.
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