Erdos Number Calculator
A tool to understand the concept of collaborative distance in academia.
This calculator uses a small, predefined sample collaboration network for demonstration purposes.
What is an Erdos Number?
The Erdos number calculator helps illustrate a fascinating concept from mathematics and social network theory. An Erdos number describes the “collaborative distance” between a person and the highly prolific Hungarian mathematician Paul Erdős. It’s a way of measuring how closely connected a researcher is to Erdős through a chain of co-authored academic papers.
Paul Erdős himself has an Erdos number of 0. Anyone who co-authored a paper directly with him has an Erdos number of 1. A person who wrote a paper with one of Erdős’s co-authors (but not with Erdős himself) has an Erdos number of 2, and so on. If a person is not connected to the Erdős collaboration network by any path, their number is considered infinite. This concept is a tribute to Erdős’s massive output of over 1,500 papers and his nomadic, collaborative style.
The Erdos Number “Formula” and Explanation
There isn’t a traditional mathematical formula for the Erdos number. Instead, it is determined by finding the shortest path in a graph—a process known as a Breadth-First Search (BFS) algorithm. The “graph” consists of nodes (authors) connected by edges (co-authoring a paper).
The logic is as follows:
- E(p) = 0, if ‘p’ is Paul Erdős.
- E(p) = min(E(c)) + 1, where ‘c’ is any co-author of person ‘p’.
This means your Erdos number is one greater than the smallest Erdos number among all your direct collaborators. For those interested in graph theory, check out this guide to network analysis.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| E(p) | The Erdos number of a person ‘p’. | Unitless Integer | 0 to ~15 (finite numbers) |
| Graph Path | The chain of co-authors connecting a person to Paul Erdős. | List of Names | Varies |
| Collaboration | The act of co-authoring a published academic paper. | Binary (Yes/No) | N/A |
Visualizing Erdos Numbers in our Sample Network
Practical Examples
Using our demonstration calculator, let’s look at two examples.
Example 1: Calculating for ‘Noga Alon’
- Input: Select “Noga Alon” from the dropdown.
- Result: Erdos Number of 1.
- Path: Noga Alon → Paul Erdős.
- Explanation: The result is 1 because Noga Alon is in our sample dataset as a direct co-author of Paul Erdős.
Example 2: Calculating for ‘William T. Gowers’
- Input: Select “William T. Gowers” from the dropdown.
- Result: Erdos Number of 2.
- Path: William T. Gowers → Béla Bollobás → Paul Erdős.
- Explanation: The calculator finds that Gowers co-authored with Béla Bollobás, who in turn co-authored with Paul Erdős. The shortest path has two steps, so the Erdos number is 2. Understanding such paths is a core part of social network analysis.
How to Use This Erdos Number Calculator
- Select an Author: Click the dropdown menu. You will see a list of authors from our sample collaboration network.
- Choose an Author: Click on the name of the author whose Erdos number you wish to find.
- View the Results: The calculator will automatically display the result.
- The Primary Result shows the calculated Erdos number.
- The Collaboration Path shows the chain of authors connecting your selection to Paul Erdős.
- Reset: Click the “Reset” button to clear the selection and results.
This tool is primarily for educational purposes to demonstrate how a shortest-path algorithm works in the context of an Erdos number calculator.
Key Factors That Affect an Erdos Number
An individual’s Erdos number is not static and depends on the entire web of academic collaborations. Key factors include:
- Field of Study: Mathematicians, particularly in fields like combinatorics and number theory where Erdős was active, are more likely to have a low Erdos number.
- Prolific Collaborators: Collaborating with someone who has a very low Erdos number (a “hub” in the network) is the fastest way to lower your own.
- Career Span: Researchers who were active during the same time as Erdős or his direct collaborators have a higher chance of a lower number.
- Definition of Collaboration: The rules for what counts as a co-authored paper can affect the graph. Our collaboration graph visualization tool can help explore these connections.
- Completeness of Data: A real-world Erdos number depends on a comprehensive database of publications, like the one maintained by the American Mathematical Society.
- Time: As new papers are published, new connections are formed, which can change Erdos numbers for many people in the network.
Sample Collaboration Data
The table below shows a small subset of the collaboration data used by this calculator to find the shortest path to Paul Erdős.
| Author | Direct Co-Authors in This Network |
|---|
Frequently Asked Questions (FAQ)
What does an Erdos number of infinity mean?
An Erdos number of infinity means that, within the known collaboration graph, there is no path of co-authorships connecting that person to Paul Erdős.
Can my Erdos number change?
Yes. If you or any author in your collaboration path publishes a new paper with someone who has a lower Erdos number, your own number could decrease.
Who has an Erdos number of 1?
The 511 mathematicians who co-authored a paper directly with Paul Erdős have an Erdos number of 1. This calculator includes a few of them, such as Noga Alon and Fan Chung.
Is a lower Erdos number better?
It is mostly a point of interest or a fun metric among mathematicians. While a low number indicates a certain closeness to the central figure of 20th-century mathematics, it is not a formal measure of a researcher’s quality or impact. Check out our article on bibliometrics for more on academic metrics.
How is this different from a real Erdos number calculator?
A true Erdos number calculator, like the one offered by MathSciNet, uses a massive, constantly updated database of nearly all mathematical publications. This tool uses a small, static, and pre-defined network for demonstration.
What is an Erdos-Bacon number?
It’s a playful metric that is the sum of a person’s Erdos number and their Bacon number (which measures collaborative distance to actor Kevin Bacon). It applies to the small group of people who have both published academic papers and appeared in films.
What algorithm is used to calculate the Erdos number?
The standard method is a Breadth-First Search (BFS) algorithm, which is guaranteed to find the shortest path in an unweighted graph like the collaboration network.
Why was Paul Erdős chosen as the center of this network?
Because of his extraordinary prolificacy and his highly collaborative nature. He co-authored papers with over 500 different mathematicians, making him a central “hub” in the social network of mathematics. For more fun facts, see our page on {related_keywords}.