The complex connectivity structure unique to the brain network is believed to underlie its robust and efficient coding capability. Specifically, neuronal networks at multiple scales utilize their structural complexities to achieve different computational goals. By analyzing an anatomical, mesoscopic mouse brain connectome based on viral tracing experiments, I will first introduce computational implications that can be inferred from a weighted and directed graph representation of the mouse brain network. Then, I will consider a more detailed and realistic network representation of the brain featuring multiple types of connection between a pair of brain regions, which enables us to uncover the hierarchical structure of the brain network using an unsupervised method.  Finally, I will discuss the relationship between the anatomical connectivity and functional networks of the mouse brain based on correlated neural activities, whose complexity is modulated by stimulus types and behavioral states