  Given the untapped potential for continuous improvement of examinations,
quantitative investigations of examinations could guide efforts to considerably
improve learning efficiency and evaluation and thus greatly help both learners
and educators. However, there is a general lack of quantitative methods for
investigating examinations. To address this gap, we propose a new metric via
complex networks; i.e., the knowledge point network (KPN) of an examination is
constructed by representing the knowledge points (concepts, laws, etc.) as
nodes and adding links when these points appear in the same question. Then, the
topological quantities of KPNs, such as degree, centrality, and community, can
be employed to systematically explore the structural properties and evolution
of examinations. In this work, 35 physics examinations from the NCEE
examination spanning from 2006 to 2020 were investigated as an evidence. We
found that the constructed KPNs are scale-free networks that show strong
assortativity and small-world effects in most cases. The communities within the
KPNs are obvious, and the key nodes are mainly related to mechanics and
electromagnetism. Different question types are related to specific knowledge
points, leading to noticeable structural variations in KPNs. Moreover, changes
in the KPN topology between examinations administered in different years may
offer insights guiding college entrance examination reforms. Based on
topological quantities such as the average degree, network density, average
clustering coefficient, and network transitivity, the Fd is proposed to
evaluate examination difficulty. All the above results show that our approach
can comprehensively quantify the knowledge structures and examination
characteristics. These networks may elucidate comprehensive examination
knowledge graphs for educators and guide improvements in teaching.
