Paul Erdős (1913-1996) was one of the most prolific mathematicians of all time, having written about 1500 mathematical articles during his lifetime, mainly with co-authors. Due to his immense output and large number of collaborators (numbering 509), the concept of the Erdős number was concieved as a way to describe the “collaborative distance” between authors of mathematical papers. For example, Erdős himself has an Erdős number of 1; a coauthor for one of his papers would have an Erdős number of 1; someone who has collaborated with a person with Erdős number of 1 (but not with Erdős himself) would have an Erdős number of 2, and so on. In other words, an Erdős collaboration graph can be drawn with paper authors as nodes and the papers edges. The Erdős number is then the shortest path from a certain node to Erdős himself.A more interesting way to look at the Erdős collaboration graph was suggested by Michael Barr ofMcGill
University in his article Rational Erdős Numbers (http://www.oakland.edu/enp/barr.pdf). He proposed that instead of simply assigning an Erdős number of 1 to each of Erdős’ direct coauthors, we can look at the exact number of papers they have collaborated on and take the reciprocal of that. For example, a person, A,  who has coauthored 4 papers with Erdős will have an Erdős number of 1/4. Lets say another person, B, then coauthors 3 papers with A. His Erdős number will be 1/4 + 1/3 = 7/12. Letting the Erdős number have non-integer values based on how “closely connected” each person is to Erdős and his collaborators makes the task of computing the Erdős number infintely more complex, especially when we consider the fact that many of the collaborators have collaborated among themselves.Michael Barr then suggested a remarkable physical interpretation of the graph. He proposed that we replace the edges between nodes with 1 ohm resistors. The Erdős number would then be the effective resistance between Erdős and the particular node in question. The network can be analyzed using a set of simultaneous equations given by Kirchhoff’s laws. It is interesting how modelling a social network between people as an electrical network simplifies the picture and enables us to have a more intuitive grasp of the network. It is noted, however, that although this allows us to use established electrical laws on the network, computing such a large number of simultaneous equations may not be practical.