Check for Isomorphism in Hypergraphs

In summary, the conversation discusses different methods for checking whether two hypergraphs are isomorphic. The brute force method is slow, and a friend suggests using bipartite graphs instead. However, there is uncertainty about whether non-isomorphic hypergraphs could have isomorphic bipartite graphs. The idea of using Whitney theorem is also mentioned, but there is not enough familiarity with the theorem for hypergraphs. The conversation ends with a hope for a readily available algorithm for checking isomorphism in hypergraphs.
  • #1
Jerrynap
8
0
Hi,

I was trying to check whether two hypergraphs are isomorphic to each other using MATLAB. I did the brute force method by permuting the vertices and check all the permutations one by one. This method is pretty slow.

An idea suggested by my friend was to represent the hypergraphs as bipartite graphs and check whether the two bipartite graphs are isomorphic instead. However, we are unsure whether two non-isomorphic hypergraphs might have isomorphic bipartite graphs. Can someone enlighten us about this?

Furthermore, we thought of applying Whitney theorem to check for isomorphism, but we are not familiar with the theorem for hypergraph.

Of course it will be best if there is a readily available algorithm to check for isomorphism in hypergraphs. :)
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

FAQ: Check for Isomorphism in Hypergraphs

1. How do you define isomorphism in hypergraphs?

Isomorphism in hypergraphs refers to the concept of two hypergraphs being structurally identical, with the only difference being the labeling of the vertices and/or edges. This means that the same connections and relationships between the vertices and edges can be found in both hypergraphs, but with different labels assigned to them.

2. Why is checking for isomorphism in hypergraphs important?

Checking for isomorphism in hypergraphs is important for various reasons, including pattern recognition, data analysis, and problem solving. It allows us to identify and compare similarities between different hypergraphs, which can help us understand the underlying structure and relationships within the data.

3. What are the main methods for checking isomorphism in hypergraphs?

The main methods for checking isomorphism in hypergraphs include the adjacency matrix method, the incidence matrix method, and the canonical labeling method. Each method has its own advantages and disadvantages, and the choice of method depends on the specific characteristics and size of the hypergraphs being compared.

4. Are there any challenges in checking for isomorphism in hypergraphs?

Yes, there are several challenges in checking for isomorphism in hypergraphs. One of the main challenges is the exponential complexity of the problem, which means that the time and resources required for analyzing larger hypergraphs can be significant. Another challenge is the existence of non-trivial automorphisms, which can complicate the process of identifying isomorphic hypergraphs.

5. How is checking for isomorphism in hypergraphs related to other graph theory concepts?

Checking for isomorphism in hypergraphs is closely related to other graph theory concepts such as subgraph isomorphism, graph homomorphism, and graph isomorphism. These concepts all involve comparing the structure and relationships between graphs, but with different levels of restrictions and requirements. Hypergraphs, being a generalization of graphs, can also be seen as an extension of these concepts.

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