I want to calculate hub scores for nodes in a network. I'm using igraph in R and the function "hub_score". Within this function is the argument "scale" which can be set to TRUE or FALSE. If I set it to TRUE, is the highest hub score in the network always 1 and the lowest hub score always 0?
I'm confused because I get 1 as highest value. But for example in "Fowler et al. 2007. Social Networks in Political Science: Hiring and Placement of Ph.D.s, 1960-2002" they got 0.52 as highest value.
Since hub (and authority) scores are the entries of an eigenvector, their magnitude is meaningless in isolation. The value assigned to a vertex is only meaningful in relation to the values of other vertices in the same graph.
scale=TRUE normalizes the hub score vector, i.e. multiplies it by an appropriate constant, so that the largest value (in magnitude) would be 1.
Note: Future versions of igraph will drop the scale parameter and will always scale the result so that the highest magnitude value is 1.