I had an interesting interaction on Twitter today. I’m doing some research with a student that involves a little graph theory. We needed some graph theory terminology that I was sure was well-known (but not known to us), so I turned to Twitter.
Let be a vertex of directed graph. Define to be the set of all vertices that point to and to be the set of all vertices that points to.
For example, in the graph below and .
My question was: what do we call the sets and ?
I received quite a few replies, and quickly discovered that there is no standard terminology. Here’s what I heard:
|incoming vertices||outgoing vertices|
|backward star||forward star|
While I thought there would be one answer, I guess it isn’t too surprising that there isn’t—we can’t even decide on basic terminology: graph/network, vertex/node, etc. There are many places in mathematics in which there are multiple names or symbols for the same mathematical object. Just think of all the ways to write the derivative: , , , and (and calculus is much older than graph theory). Even multiplication can be expressed in multiple ways: , , and .
Maybe we should institute a mathematical standards board…. nah!