The downside of "Katz centrality" compared to PageRank appears to be that if if a big node links to many many nodes, all of those earn a lot of reputation, regardless of how outgoing links there are:
Katz centrality is a measure of the relative influence of a node within a network. It extends the concept of degree centrality by considering not just the immediate connections (i.e., the direct neighbors of a node) but also the broader network, taking into account the influence of nodes that are connected to a node's neighbors. The fundamental idea behind Katz centrality is that a node is considered important not only because it has many direct connections but also because its connections lead to other connected nodes.
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