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Weiqi, also called Go or Baduk, is regarded as the most complicated board game in the world. Weiqi playing has a very long history in East Asia. Its strategic thinking in decision-making even affects militarists there. The availability of the records of almost all Weiqi games in the past decades enables us to perform quantitative studies about this sport with high statistical significance. Here, we construct the directed and undirected Elo transfer networks using over 80,000 Weiqi game records from 1941 to 2019. We investigate the distributions of network measures of the two Elo transfer networks, such as node degree, clustering coefficient, betweenness centrality, and closeness centrality. We find a strong correlation between the average Elo value of a Weiqi player and a few node traits. We also find a rich-club phenomenon among high-Elo players. The two networks are unveiled to possess significant communities, which are consistent with each other and can be well interpreted by player's affiliation, gender, and Elo value. These findings are different in a large part from those of the chess Elo transfer networks. [ABSTRACT FROM AUTHOR]