Erdos-Bacon Number
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Let us define the following numbers:

"Erdős number" is the degrees of separation from mathematician
Paul Erdős (1913–1996), as measured by joint authorship of papers.
In other words, Paul Erdős himself has Erdős number 0.
Erdős' co-authors have Erdős number 1, obviously a closed list which
you can retrieve from the Erdős Number Project [1]. The co-authors of
these people have Erdős number 2.
The co-authors of Erdős-2 authors have upper bound 3 for their Erdős
number, since they might co-author with an Erdős-1 author in the
future. And so on, recursively.

What makes Paul Erdős a good rank-0 for this definition is that he has
co-authored articles with a large and diverse set of people.

Similarly, "Bacon number" is the degrees of separation from Kevin
Bacon as measured by being credited as actors in the same film.
Like Erdős, Bacon has starred in many films from different genres
which makes him a good base for rank-0.

Finally, "Erdős-Bacon number" is the sum of the two. There is a small
number of people who have a finite Erdős-Bacon number, the relevant
Wikipedia page lists some [2].

One very interesting example, at least from a KR point of view,
is Natalie Portman who has an Erdős-Bacon number of at most 7:

Sarah Michelle Gellar has Bacon number 1,
"The Air I Breathe", 2007.

Natalie Portman has Bacon number at most 2,
A Powerful Noise Live, 2009

Joseph Gillis has Erdős number 1, [1]
Jonathan Victor has Erdős number 2, doi:10.1137/0513062
Michael Gazzaniga has Erdős number at most 3 [3]
Abigail Baird has at most 4, doi:10.1162/0898929053467569
Natalie Hershlag has at most 5, doi:10.1006/nimg.2002.1170

Natalie Portman and Natalie Hershlag are the same person.

The exercise is to:

(a) Import bibliography and filmography dumps into a knowledge
graph. Write some common-sense knowledge that will allow an inference
engine to decide if two entities from different databases might refer
to the same person or cannot possibly refer to the same person.

(b) Use this KG to find persons with finite Erdős-Bacon number.
Validate the axioms you have authored: Are the Wikipedia examples
retrieved? If not, why not? Are further persons discovered by your
system correctly identified as having finite Erdős-Bacon number?
Note that the point is not that you retrieve everybody, but that
you correctly identify what worked and what didn't and why.

(c) Bonus question: Use GenAI to generate the properties of a
hypothetical movie (title, genre, director, partial cast) or article
(title, journal, authors) that would reduce the Erdős-Bacon number
upper bound for somebody with a finite Erdős-Bacon number. Validate
that the movie or article is consistent with the KG and argue whether
it is realistic or not.

References

[1] https://sites.google.com/oakland.edu/grossman/home/the-erdoes-number-project

[2] https://en.wikipedia.org/wiki/Erdős–Bacon_number

[3] https://nyuscholars.nyu.edu/en/publications/acquired-central-dyschromatopsia-analysis-of-a-case-with-preserva