  Based on the previously proposed concept Understanding Tree, this paper
introduces two concepts: Understanding Graph and Understanding Map, and
explores their potential applications. Understanding Graph and Understanding
Map can be deemed as special cases of mind map, semantic network, or concept
map. The two main differences are: Firstly, the data sources for constructing
Understanding Map and Understanding Graph are distinctive and simple. Secondly,
the relations between concepts in Understanding Graph and Understanding Map are
monotonous. Based on their characteristics, applications of them include
quantitatively measuring a concept's complexity degree, quantitatively
measuring a concept's importance degree in a domain, and computing an optimized
learning sequence for comprehending a concept etc. Further study involves
evaluating their performances in these applications.
