Hi, thank you for making this video which is very useful in my studies. But i have one doubt in line graph that is what if the intersection of hyperedges contain more than one vertices? for example let e_1 and e_2 are hyperedges and there intersection is more than 1 vertices, so then what about the line graph?
Hi, great question. If the intersection is more than 1 vertex, in the line graph e_1 and e_2 are still made adjacent. The definition of adjacency in a line graph only requires that the edges share at least one incident vertex.
Hi, this series is very useful thank you for making this! I have a very specific technical question if you don't mind me asking. I work on an algorithm which analyzes the 3-line graph of our hypergraph structured data, which is the line graph except you only include edges for hyperedge intersections which have at least 3 vertices. I have found that if you associate every edge in the 3-line graph with the vertices that form the corresponding connection between hyperedges, you can define each set of these vertices as a hyperedge and construct another hypergraph, which seems to have very interesting properties. Does that make sense? Is there some hypergraph theory that describes such an operation? I have not been able to find it thus far. Thank you again!
You're very welcome, and interesting question! If I understand correctly, the sets of vertices that make up an (intersection with 3+ vertices) of hyperedges in your original hypergraph become your new hyperedges, and the vertices of the new hypergraph are still the same as the vertices of the original hypergraph?
@@pswjt1266 Hello again! I looked around but could not find anything matching the operation you described, but this is similar and may be of interest: arxiv.org/abs/1901.06292 I think you could perform their "edge intersection hypergraph" operation and then weakly delete any edges with exactly 2 vertices to get the same result as your new operation, except you would miss all of the submaximal intersecting sets of vertices of size 3+ present in your original hypergraph.
Hi i really enjoy watching your videos on hypergraph, which are so informative and intuitive. Recently, I got confused about the concept "similarity" and the similarity function in hypergraph. Will you cover this topics in your future videos?
Hello, thanks for reaching out, I'm glad that you enjoy my videos! I'm not familiar with the similarity concept regarding hypergraphs, could you please direct me to the paper/papers discussing this topic? I can try to look it over and cover the topic in a future video.
@@VitalSine Thanks for your reply! The relevant content is in Chapter 1.3.2 of this book: "Bretto, A. (2013). Hypergraph theory. An introduction. Mathematical Engineering. Cham: Springer". Looking forward to seeing your new videos in this series!
![Guide to Hypergraph Walks, Trails, and Paths [Hypergraph Episode 6]](http://i.ytimg.com/vi/G9TkLOTftms/mqdefault.jpg)
![Guide to Hypergraph Walks, Trails, and Paths [Hypergraph Episode 6]](/img/tr.png)
![Introduction to Hypergraphs [Graph Theory]](http://i.ytimg.com/vi/UwvZn9lm_98/mqdefault.jpg)
Hi, thank you for making this video which is very useful in my studies. But i have one doubt in line graph that is what if the intersection of hyperedges contain more than one vertices? for example let e_1 and e_2 are hyperedges and there intersection is more than 1 vertices, so then what about the line graph?
Hi, great question. If the intersection is more than 1 vertex, in the line graph e_1 and e_2 are still made adjacent. The definition of adjacency in a line graph only requires that the edges share at least one incident vertex.
i NEED the video on cliques of hypergraphs and 2-section graphs!
A conformal hypergraph video is coming soon, we'll look at a lot of concepts surrounding cliques of 2-sections and the hypergraph edges 👍
Hi, this series is very useful thank you for making this! I have a very specific technical question if you don't mind me asking. I work on an algorithm which analyzes the 3-line graph of our hypergraph structured data, which is the line graph except you only include edges for hyperedge intersections which have at least 3 vertices. I have found that if you associate every edge in the 3-line graph with the vertices that form the corresponding connection between hyperedges, you can define each set of these vertices as a hyperedge and construct another hypergraph, which seems to have very interesting properties. Does that make sense? Is there some hypergraph theory that describes such an operation? I have not been able to find it thus far. Thank you again!
You're very welcome, and interesting question! If I understand correctly, the sets of vertices that make up an (intersection with 3+ vertices) of hyperedges in your original hypergraph become your new hyperedges, and the vertices of the new hypergraph are still the same as the vertices of the original hypergraph?
@@VitalSine Yes exactly!
@@pswjt1266 Hello again! I looked around but could not find anything matching the operation you described, but this is similar and may be of interest: arxiv.org/abs/1901.06292
I think you could perform their "edge intersection hypergraph" operation and then weakly delete any edges with exactly 2 vertices to get the same result as your new operation, except you would miss all of the submaximal intersecting sets of vertices of size 3+ present in your original hypergraph.
@@VitalSine This does indeed seem close to what I have in mind! Thank you so much!
@@pswjt1266 You're very welcome, and thank you for sharing this new operation with me.
Hi i really enjoy watching your videos on hypergraph, which are so informative and intuitive. Recently, I got confused about the concept "similarity" and the similarity function in hypergraph. Will you cover this topics in your future videos?
Hello, thanks for reaching out, I'm glad that you enjoy my videos! I'm not familiar with the similarity concept regarding hypergraphs, could you please direct me to the paper/papers discussing this topic? I can try to look it over and cover the topic in a future video.
@@VitalSine Thanks for your reply! The relevant content is in Chapter 1.3.2 of this book: "Bretto, A. (2013). Hypergraph theory. An introduction. Mathematical Engineering. Cham: Springer". Looking forward to seeing your new videos in this series!