1、总体结构：
主句：Barbara's academic major is history
非限制性定于从句：which is second only to political science as the most popular major among liberal arts students
2、主句：
主语：Barbara's academic major
系动词：is
表语：history
3、非限制性定于从句：
先行词：history
引导词：which,在从句中做主语
系动词：is
is second only to是“仅次于的意思”,to在此处是介词,political science
是to的宾语
as做介词,引导the most popular major among liberal arts students,修饰的是political science