Knowledge graph is a hot topic in artificial intelligence area and has been widely adopted in intelligent search and question-and-answer system. Knowledge graph can be regarded as a complex network system and analyzed by complex network theory, which studies the interaction or relationship between various factors and basic characteristics of complex system. Its characteristics and their physical meanings are very helpful in understanding the nature of the knowledge graph. Concept graph is a large-scaled knowledge graph published by Microsoft. In this paper, we construct a huge complex network according to Microsoft’s concept graph. Its complex network characteristics, such as degree distribution, average shortest distance, clustering coefficient and degree correlation, are calculated and analyzed. The concept graph is not a connected network and its scale is very large; an approach is proposed to extract its largest connected subnet. The method has obvious advantages in both time complexity and space complexity. In this paper, we also present a method of calculating the approximate average shortest path of the largest connected subnet. The method estimates the maximum and minimum value of the shortest distance between nodes according to the distance between the central node and the network layer that the node belongs to and the distance between different layers. In order to calculate the clustering coefficient, different methods are introduced for nodes with different degree values and Map/Reduce idea is adopted to reduce the time cost. The experimental results show that the largest subnet of the concept graph is an ultra-small world network with the characteristics of scale-free. The average shortest path length decreases towards 4 with the network size increasing, which can be easily explained by the diamond-shaped network structure. The concept graph is a disassortative network where low degree nodes tend to connect to high degree nodes. The subConcepts account for 99.5% of nodes in the innermost k-core after k-shell decomposition. It shows that the subConcepts play an important role in the connectivity of network. The absence of subConcept affects the complexness of concept graph most, the concept next, and the instance least. The 82% instance nodes and 40% concept nodes of the concept graph each have a degree value of 1. It is believed that compared with the concept words, the instance words do not lead to the ambiguity in the understanding of natural language, caused by polysemy.