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Hello,
I believe there's a mistake in your documentation in the personalized eigenvector centrality part. You have the following:
Personalized Eigenvector Centrality is a variation of Eigenvector Centrality which is biased towards a set of sourceNodes. By default, the power iteration starts with the same value for all nodes: 1 / |V|. For a given set of source nodes S, the initial value of each source node is set to 1 / |S| and to 0 for all remaining nodes.
But the example you have on the same page (for the given toy graph) assumes the initial value for all nodes as 1, not 1 / |V|, which is actually the right convention for eigenvector centrality computation. I verified this by NetworkX. I haven't checked your API but if the results are produced by it, it's also correct. This also means that in the personalized case, the initial value of each source node should be set to 1 as well.
So please update the above part accordingly.