What kind of networks is the eigenvector centrality made for?

Question

I was researching on different centrality measures and had a question regarding the eigenvector centrality: In what type of network is it better to use the eigenvector centrality than the degree centrality? I am particularly interested in examples.

Answer 1

What centrality is best to use does not primarily on your network but on your underlying question, i.e., what you are using the centrality for. For many applications the degree centrality’s problem is that it does not look further than one edge. For example, the degree centrality would consider the centre of an otherwise badly connected star sub-network highly central, while the eigenvector centrality wouldn’t.

A good practical example is Google Page Rank, which is based on the eigenvector centrality. Suppose you run a major Internet search engine and want to order web sites (i.e., nodes in the World Wide Web) by centrality to determine the order of search results. Being on the top of search results is very important to some people for marketing reasons, hence they are willing to go to lengths to manipulate it. Therefore your centrality needs to be robust against such efforts to ensure the quality of your service.

Now, if you used the degree centrality, an easy strategy of manipulation would be: Create a lot of bogus web sites that all link to your site. This would be the equivalent of the star sub-network mentioned above. The eigenvector centrality is not vulnerable to this kind of attack as the bogus sites have a very low centrality and thus their links do not contribute much centrality to your main web site. A link from a highly central web site like Stack Exchange is much more valuable than this (which is so many people try to smuggle links to their web sites onto this site).