Dynamic Katz Centrality
Because of its simplicity, Katz Centrality has become one of the most established centrality measurements. The definition of Katz centrality is that it presents the amount of influence by summing all walks starting from the node of interest and weighting walks by some attenuation factor smaller than 1.
Many of today's real-world networks evolve at a great pace over time. The constant change of information leads to the dynamic environment and creation of methods that can handle a large amount of data and provide quick results on updates.
Visualization of the Katz centrality progression through time. Warmer colored nodes represent the higher values for Katz centrality measurement.
The explanation of Dynamic Katz Centrality is presented in the paper by Alexander van der Grinten et. al. and Twitter. The paper is worth reading at Scalable Katz Ranking Computation in Large Static and Dynamic Graphs.
Dynamic Katz Centrality is implemented as part of the MAGE project. Be sure to check it out in the link above. ☝️
The best fit for dynamic Katz centrality is social network analysis. The importance and decay of walk propagation are intuitively similar to the message propagation in social networks. To work with the scale of today's social networks like Twitter, dynamic algorithm implementations need to be used. The Katz centrality algorithm performs on a similar level of precision in determining influence when compared to human experts in the field.