I don't understand why this is called an illusion. How about just counting the edges as a measure of popularity? Surely nothing "appears to be more popular" than it is -- if there are more outgoing edges to other nodes, it is more popular. Popularity has always been about popular people.
Because each node's view of neighboring nodes is a biased sample of the global data set.
A related example: the average person is less popular than their average friend, and therefore feels that they are below average popularity. This happens since popular people are weighted more heavily in the sampling, but people don't realize they are confusing the local average with global average.
