In graph theory, centrality is any measure that determines how structurally important a node is within a graph.
Katz Centrality computes the influence of a node by calculating the number of neighbours, and other nodes on the graph that connect to the node through these immediate neighbours. Connections made with distant neighbours are penalised by an attenuation factor. It is a variation of Eigenvector Centrality that incorporates the direction of transactions.
There is major drawback to using Katz Centrality - if a node with high centrality is pointing to lots of other nodes, they will also get high centrality. e.g. If you have a node on your graph with over 1000 neighbours and this node has a high centrality, all of those neighbours would also score highly, which would not be especially useful analytically. PageRank Centrality, the algorithm used by Google to rank search results, attempts to resolve this issue by evenly distributing the centrality a node has to share.