Consuming news from social media is becoming increasingly popular. However, social media also enables the wide dissemination of fake news. Because of the detrimental effects of fake news, fake news detection has attracted increasing attention. However, the performance of detecting fake news only from news content is generally limited as fake news pieces are written to mimic true news. In the real world, news pieces spread through propagation networks on social media. The news propagation networks usually involve multi-levels. In this paper, we study the challenging problem of investigating and exploiting news hierarchical propagation network on social media for fake news detection. In an attempt to understand the correlations between news propagation networks and fake news, first, we build hierarchical propagation networks for fake news and true news pieces; second, we perform a comparative analysis of the propagation network features from structural, temporal, and linguistic perspectives between fake and real news, which demonstrates the potential of utilizing these features to detect fake news; third, we show the effectiveness of these propagation network features for fake news detection. We further validate the effectiveness of these features from feature importance analysis. We conduct extensive experiments on real-world datasets and demonstrate the proposed features can significantly outperform state-of-the-art fake news detection methods by at least 1.7% with an average F1>0.84. Altogether, this work presents a data-driven view of hierarchical propagation network and fake news and paves the way towards a healthier online news ecosystem.