The global rise of COVID-19 health risk has triggered the related misinformation infodemic. We present the first analysis of COVID-19 misinformation networks and determine few of its implications. Firstly, we analyze the spread trends of COVID-19 misinformation and discover that the COVID-19 misinformation statistics are well fitted by a log-normal distribution. Secondly, we form misinformation networks by taking individual misinformation as a node and similarity between misinformation nodes as links, and we decipher the laws of COVID-19 misinformation network evolution: (1) We discover that misinformation evolves to optimize the network information transfer over time with the sacrifice of robustness. (2) We demonstrate the co-existence of fit get richer and rich get richer phenomena in misinformation networks. (3) We show that a misinformation network evolution with node deletion mechanism captures well the public attention shift on social media. Lastly, we present a network science inspired deep learning framework to accurately predict which Twitter posts are likely to become central nodes (i.e., high centrality) in a misinformation network from only one sentence without the need to know the whole network topology. With the network analysis and the central node prediction, we propose that if we correctly suppress certain central nodes in the misinformation network, the information transfer of network would be severely impacted.