A novel approach combining time series analysis and complex network theory is proposed to deeply explore characteristics of the COVID-19 pandemic in some parts of the United States (US). It merges as a new way to provide a systematic view and complementary information of COVID-19 progression in the US, enabling evidence-based responses towards pandemic intervention and prevention. To begin with, the Principal Component Analysis (PCA) varimax is adopted to fuse observed time-series data about the pandemic evolution in each state across the US. Then, relationships between the pandemic progress of two individual states are measured by different synchrony metrics, which can then be mapped into networks under unique topological characteristics. Lastly, the hidden knowledge in the established networks can be revealed from different perspectives by network structure measurement, community detection, and online random forest, which helps to inform data-driven decisions for battling the pandemic. It has been found that states gathered in the same community by diffusion entropy reducer (DER) are prone to be geographically close and share a similar pattern and tendency of COVID-19 evolution. Social factors regarding the political party, Gross Domestic Product (GDP), and population density are possible to be significantly associated with the two detected communities within a constructed network. Moreover, the cluster-specific predictor based on online random forest and sliding window is proven useful in dynamically capturing and predicting the epidemiological trends for each community, which can reach the highest.