A very interesting analysis of these regions from New Geography, and Sacramento is included in the graph about halfway down, after the jump (small print).
The fortunes of U.S. core cities (municipalities) have varied greatly in the period of automobile domination that accelerated strongly at the end of World War II. This is illustrated by examining trends between the three categories of “historical core municipalities” (Figure 1). Since that time, nearly all metropolitan area (the functional or economic definition of the city) growth has been suburban, outside core municipality limits, or in the outer rings of existing, core municipalities.
Approximately 26 percent of major metropolitan area population is located in the core municipalities. Yet, many of these municipalities include large areas of automobile orientation that are anything but urban core in their urban form. Most housing is single-detached, as opposed to the much higher share of multi-family in the urban cores, and transit use is just a fraction of in the urban cores.
Even counting their essentially suburban populations, today’s core municipalities represent, with a few exceptions, a minority of their metropolitan area population. The exceptions (San Antonio, Jacksonville, Louisville, and San Jose) are all highly suburbanized and have annexed land area at a substantially greater rate than they have increased their population.
According to the 2010 census, using the 2013 geographic definitions, core cities accounted for from five percent of the metropolitan area population in Riverside-San Bernardino to 62 percent in San Antonio (Figure 2).
Retrieved May 11. 2014 from http://www.newgeography.com/content/004306-urban-core-jurisdictions-similar-label-only