What is an Erdös Number ?
Paul Erdos, the late widely-traveled and
incredibly prolific Hungarian mathematician of the highest caliber, wrote
hundreds of mathematical research papers in many different areas, many in
collaboration with others. His Erdos number is 0. His co-authors have
Erdos number 1. People other than Erdos who have written a joint paper
with someone with Erdos number 1 but not with Erdos have Erdos number 2,
and so on. If there is no chain of co-authorships connecting someone with
Erdos, then that person's Erdos number is said to be infinite. In
graph-theoretic terms, the collaboration graph C has all mathematicians as
its vertices; the vertex p is Paul Erdos. There is an edge between u and
v if u and v have published at least one mathematics article together. (We
will adopt the most liberal interpretation here, and allow any number of
other co-authors to be involved; for example, a six-author paper is
responsible for 15 edges in this graph, one for each pair of authors.
Other approaches would include using hypergraphs or multigraphs or
multihypergraphs.) The Erdos number of v, then, is the distance (of the
shortest path) in C from v to p. The set of all mathematicians with a
finite Erdos number is called the Erdos component of C. It has been
conjectured that the Erdos component contains almost all present-day
publishing mathematicians (and has a not very large diameter), but perhaps
not some famous names from the past, such as Gauss. Clearly, any two
people with a finite Erdos number can be connected by a string of
co-authorships, of length at most the sum of their Erdos numbers.
My link is from Daniel J. Kleitman(1) to Albert R Meyer(2) to me(3).
Link to the
Erdös Number Homepage.