We propose a non-metric measure of the “closeness” felt between two nodes in an
undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a realvalued Generalized Erd¨os Number (GEN). While our measure is developed with a collaborative
network in mind, the approach can be of use in a variety of artificial and real-world networks.
We are able to distinguish between network topologies that standard distance metrics view as
identical, and use our measure to study some simple analytically tractable networks. We show
how this might be used to look at asymmetry in authorship networks such as those that inspired
the integer Erd¨os numbers in mathematical coauthorships. We also show the utility of our approach
to devise a ratings scheme that we apply to the data from the NetFlix prize, and find a significant
improvement using our method over a baseline