Topological analysis of knowledge maps

A knowledge map can be viewed as a directed graph, in which each node is a knowledge unit (KU), and each edge is a learning-dependency between two KUs. Understanding the topological properties of knowledge map can help us gain better insights into human cognition structure and its mechanism, design better knowledge map construction algorithms, and guide learners' navigational learning through knowledge map. In this paper, we perform topological analysis on 12 knowledge maps from computer science, mathematics, and physics. We discover that they exhibit small-world and scale-free properties like many other networks. Specifically, we show the locality of learning-dependency and hierarchical modular structure in the 12 knowledge maps. In addition, we study how KUs affect the network efficiency by removing KUs based on different centrality measures. We find that the importance of KUs varies greatly.