Is PageRank always better then eigenvector or Katz centrality?

Question

As far as I understand, there is classical eigenvector centrality and there are variants such as Katz centrality or PageRank. I wonder if the latter is the "latest stage" in the evolution of eigenvector centrality and therefore always superior? Or are there certain conditions, depending on which one should use one or the other. If so, what conditions would that be?

Whitman

What do you mean exactly by "superior"? – Tiffinytiffy

Answer 1

Might be a little bit late, but

Eigen Vector Centrality assumes that nodes with more important connections are important. For example, people who know the president are probably important. mathematically, this is performed by calculating the centrality measurements by finding the eigen vector of the largest eigenvalue of the adjacency matrix.

The problem with Eigen Vector Centrality is that it does not handle directed graphs well as centrality is not passed to incoming edges, leading to lots of zeroes for centrality despite having many outgoing edges. Katz Centrality seeks to fix this problem by adding a small bias term so that no node has strictly zero centrality, thus affecting the centralities of the neighboring nodes as well.

However, the problem with Katz Centrality is that when a node becomes very central in a network, it passes its centrality to all of its outgoing links, making all those nodes very popular. For example, even though people who know the president are important, not all of them are (the car driver of the president for example). To fix this, PageRank Centrality utilizes the degree centrality of the node, mixed with Katz centrality to balance this problem.

In Conclusion, If graph is undirected, use Eigen Vector Centrality. If graph is directed, using Katz or PageRank is dependent upon the situation. If you want nodes that are extremely central to highly influence its neighbors, then use Katz; else, use PageRank.

Rheometer

Answer 2

you can not compare these three cause they are base on different prospective and definition of Centrality. PageRank uses eigenvector centrality concept to determine how important a website is read this

for instance : in eingenvector centrality we use right eigenvector in the power Iteration algorithm. Now in Pagerank algorithm, we are interesting in inlinks of nodes not outlinks(directed graph). so instead of using right eigenvector, we use left eigenvector. Eigenvector centrality Also read : Katz centrality

Silvanus