Mar 17 min read

Are you connected to Kevin Bacon? An introduction to Erdős-Bacon numbers

By Hayley Lawrence

What are bacon numbers?

Bacon numbers are an intriguing concept which determine the degrees of separation of an individual from Kevin Bacon, who is a notable actor, well known for his roles in the movies Footloose (1984) and Hollowman (2000). When calculating these numbers, Kevin Bacon himself has a bacon number of 0, those who have starred in a film directly with Kevin have a bacon number of 1, and those who have featured in a film with an individual who has a bacon number of 1, would have a bacon number of 2, and so on. Therefore, the lower the bacon number a person has, the closer they are to Kevin Bacon.

Let’s take a look at some examples:

The Oracle of Bacon, an informative website which calculates the degrees of separation of actors to Kevin Bacon and uses data from TMDB to do so, does not consider links through TV shows, writers, producers etc, meaning that their total number of linkable actors is 1,198,549, which, don’t get me wrong is still a large quantity of people. However, others may interpret the rules behind calculating bacon numbers in different ways, with a link counting if the individual has met Kevin Bacon - this signifies that the number of people with a low bacon number could be billions! For example, with a more relaxed outlook on the rules behind calculating what counts as a link, someone may consider a news reporter who attended the 2023 Vanity Fair Oscars Party at the same time that Kevin Bacon did as having a bacon number of 1, seeing as they had met the actor, even though others may argue that a link only counts between actors who star in a well known film together. That being said, it is unlikely for a notable actor to have a bacon number of more than 4, with the average currently being 3.094, as told by the Oracle of Bacon.

Kevin Bacon has reportedly been in at least 67 films, which means that he would have worked with a large number of actors within these, hence many individuals have a low bacon number of 1 or 2 due to Kevin’s wide portfolio of starring in many movies which have consequently formed many links within the industry.

The history behind Bacon numbers

The idea of bacon numbers all started in January 1994 where Bacon told Premiere magazine that “he had worked with everybody in Hollywood or someone who’s worked with them”. After this, many took to the Internet and a discussion group was formed with the heading “Kevin Bacon is the centre of the Universe”, which caught the attention of three college students in Pennsylvania. After having seen two movies one after the other which had both featured Kevin Bacon, Craig Fass, Brian Turtle and Mike Gileni created a game known as the “Six degrees of Kevin Bacon” where players choose an actor and connect them to another actor via a film that both actors have both starred in, until they are lead to the actor Kevin Bacon with the challenge being to ultimately make the least links as possible. After inventing this game, Craig, Brian and Mike wrote a letter to popular talk show host, Jon Stewart, claiming that “Kevin Bacon was the centre of the entertainment universe”, which secured them a place on The John Stewart show and The Howard Stern show where they explained the game and gained further publicity. Although he disliked the game at first, Kevin Bacon eventually found it amusing and as a result of this, wrote the introduction to the three students’ book, Six Degrees of Kevin Bacon, which was published in 1996 and is still being sold to this very day. As well as this, Endless Games, which is a renowned game publisher, released a board game based on the Bacon number concept.

Is Kevin Bacon a good centre?

When thinking about Bacon numbers, we usually only consider all the links that lead back to the actor Kevin Bacon meaning that Kevin is our centre, however, the concept could be used with other famous actors within the film business, some of which may have even better connections to the rest of the industry than Kevin Bacon himself has. Research shows that Kevin Bacon is actually the 582nd best centre within the Hollywood Universe, however, you may be wondering…what makes an actor to be a better “centre” than another?

To calculate this, we need to consider the breakdown of how many people there are with specific Bacon numbers:

Taking a look at this table, we can infer that there is one person (Kevin Bacon) with a bacon number of 0, 2119 people with a bacon number of 1, 215767 people with a bacon number of 2 etc. Therefore, to find the average Bacon number where the actor Kevin Bacon is the centre, we must do the following calculation…

This means that the average Bacon number is around 3.099.

We can now compare this to actor Samuel L. Jackson, who is currently the top centre of the Hollywood Universe and has starred in many hit films such as ‘The Incredibles’ and ‘The Avengers’.

By referring to this table, we can conclude that the average Jackson number for Samuel L. Jackson is 2.898 as we conduct the following calculation…

This implies that Jackson makes a better centre than Kevin Bacon seeing as his average number of 2.898 is lower than that of Kevin Bacon’s, therefore he has more links within the industry. There are many other well known actors who make better centres than Kevin Bacon does such as Brad Pitt, Johnny Depp and Julia Roberts; This could be due to the fact they have starred in more films so are exposed to a wider range of actors, hence have fewer links.

What are Erdős numbers

The concept of Bacon numbers also applies to Erdős numbers which describe the “collaborative distance” between an individual and Paul Erdos, a Hungarian mathematician who published many papers with solutions to challenging mathematical problems throughout his lifetime. Paul studied problems mainly linked to discrete mathematics and covered areas including graph theory, number theory, set theory and probability theory. Where a link between a person to another was through the collaboration of a film in finding out one’s bacon number, for Erdos numbers, one must be a coauthor of a research paper with another person. Paul Erdos himself would have an Erdos number of 0, and the authors who have written a joint article with him would have an Erdos number of 1. Seeing as Erdos had 509 direct collaborators throughout the 1,500 mathematical articles in which he wrote, there are 509 people who have an Erdos number of 1. Let’s take a look at the following diagram:

For this example, Eliot would have an Erdos number of 2 as Erdos wrote an article with Sandra, who wrote an article with Eliot. However, similar to the concept of Bacon numbers, there is ambiguity over what is considered a link between two people as some consider a link between two people when they co-write articles such as an obituary, which isn’t really joint work. That being said, the concept of Erdos numbers was of great help to several projects which were investigating the connectivity between various researchers and mathematicians and as a consequence, studies show that many of the leading mathematicians tend to have low Erdos numbers. Although Erdos sadly passed away in 1996, it is still possible for talented individuals to have a low Erdos number, however it will become increasinging difficult as mathematicians with low Erdos numbers will pass and therefore be unavailable to collaborate with the aspiring younger generation.

Some enthusiasts have created the idea of having an Erdos-Bacon number, which is the sum of one’s Erdos and Bacon numbers. In this case, the lower an individual’s Erdos-Bacon number is, the more connected they are to mathematician, Paul Erdos and actor, Kevin Bacon, therefore to have a low Erdos-Bacon number, the person would have to be well known in both the academic and entertainment industries.

Examples of recognisable individuals and their Erdos-Bacon numbers include:

Daniel Kleitman, who has an Erdos-Bacon number of 3, as he has an Erdos number of 1 and a Bacon number of 2
Stephen Hawking, who has an Erdos-Bacon number of 6, as he has an Erdos number of 4 and a Bacon number of 2
Kristen Stewart, who has an Erdos-Bacon number of 7, as he has an Erdos number of 5 and a Bacon number of 2

The six degrees of separation

The six degrees of separation is a theory which connotes that any person on the planet is connected to another person on the planet through a maximum of six degrees - meaning that they have no more than 5 links! In 1929, the theory was first proposed by the Hungarian writer, Frigyes Karinthy and in the 1950s, a professor and research mathematician attempted to mathematically prove that the theory is correct and they had phrased their question as:

However after two decades, they were unsuccessful in solving the problem.

A few years later, in 1967, a new way to test the theory was introduced by American sociologist Stanley Milgram which he called “the small-world problem”. In his small world experiment, Milgram selected individuals in Kansas and Nebraska to send packages to a stranger in Boston where the senders were told the recipient’s name, occupation and location. Each participant was instructed to send the package to a friend who was most likely to know the target stranger personally and this process was repeated until the package would reach its intended recipient. Surprisingly, the experiment showed that it took an average of between five and seven intermediaries for the packages to reach their desired destinations, despite many people predicting that the packages would have to go through hundreds of people before reaching their endpoints. Following the investigation, Milgram’s results were published in Psychology Today and gave rise to the term ‘Six Degrees of Separation’.

Initially, Stanley’s findings were questioned as they were only based on a small number of packages, so were deemed unreliable by some people, however after the concept of Bacon Numbers was released, the theory of people being connected in less than six links was more accepted. There have been a numerous number of challenges set out by different organisations to test the Six Degrees of Separation, such as Microsoft examining the minimum chain length required to link 180 billion distinct pairs of users in the Microsoft Messenger database in 2008, and Facebook reporting in 2016 that the average chain length among its users was 3 and a half degrees of separation.

It’s intriguing to think that this theory shows that any two people, no matter how far apart they are geographically or culturally, can be linked by around 6 mutuals (if not less!). Showcasing the interconnectivity of the World today, the theory supports the ideas of popular phrases you may already be familiar with such as ‘everyone’s connected’ and ‘it’s a small world’.

The simple concepts of Bacon, Erdos and Bacon-Erdos numbers as well as the six degrees of separation theory successfully highlight the amazing network of people around the World and it is interesting to see how the basic concepts of links and mutuals can lead to such engrossing and developed ideas.