Los Angeles doesn't really have a core part, because it's one of the most poorly designed cities on the planet. The population density is just way too low for a city of its size.
The funny thing is that if you take a look at the metro area as a whole, Los Angeles is more dense than New York. Really.
http://blogs.laweekly.com/informer/2012/03/los_angeles_density_urban_new_york_census.phpThe area is hemmed in by mountains and climate, so the suburbs are closely-packed by American standards, and you don't really have any quasi-rural exurbia to speak of.