I encourage you to look at the map on this Brookings.edu article, titled "Political rhetoric exaggerates economic divisions between rural and urban America".
The map, and the article, show that "Nearly 54 percent of people living in areas classified by the Census Bureau as rural also live in a county that is part of one of the nation’s 383 metropolitan areas."
Thus, it's the other 46% who are not closely connected to any city.
This is significant because the web library I've been building since 1993 focuses on urban issues and urban poverty and inequality. In many articles I've suggested that the largest urban areas, where school age student population is greater than 100,000 students, have unique problems caused by the number of students and the size of the bureaucracy that are different that rural areas, where lack of density and distance between students and potential support offer barrier to place based support services like non-school tutor/mentor programs.
If you're building such a library, let's connect.
Recently two resources that map poverty in the Appalachian region have come to my attention. Here's the links:
1) Community Commons web site story, Mapping Poverty in the Appalachian Region
2) Appalachian region data overview from the 2010-14 American Community Survey Chartbook
Note: Jan. 2, 2018 update
The 100 year capitalist experiment that keeps Appalachia poor, sick and stuck on coal. - article