Why not have many edges instead of one edge connecting to many nodes (in hypergraphs) [closed]

As a follow-up to What are the Applications of Hypergraphs, the linked article:

Learning with Hypergraphs: Clustering, Classification, and Embedding

Mentions this:

Let us consider a problem of grouping a collection of articles into different topics. Given an article, assume the only information that we have is who wrote this article. One may construct an undirected graph in which two vertices are joined together by an edge if there is at least one common author of their corresponding articles...

A natural way of remedying the information loss issue occurring in the above methodology is to represent the data as a hypergraph instead. A hypergraph is a graph in which an edge can connect more than two vertices . In other words, an edge is a subset of vertices. In what follows, we shall unifiedly refer to the usual undirected or directed graphs as simple graphs. Moreover, without special mentioning, the referred simple graphs are undirected. It is obvious that a simple graph is a special kind of hypergraph with each edge containing two vertices only. In the problem of clustering articles stated before, it is quite straightforward to construct a hypergraph with the vertices representing the articles, and the edges the authors (Figure 1). Each edge contains all articles by its corresponding author.

What I'm wondering is, instead of using 1 edge with many vertices, why not use many edges. That way it's just like a normal graph, not a hypergraph.

I don't yet understand the value in making 1 edge become essentially like a new type of node, if you could do the same thing by creating many edges. In hypergraphs they even call these new things "tentacles" or "attachments", connecting the edge to many things. Then it's like an edge is just another node. Hoping for some clarification on why this is necessary or what advantage this provides that multiple edges can't accomplish.

closed as off-topic by Peter Heinig, Mark Sapir, Stefan Kohl, Ben Barber, Chris GodsilFeb 26 '18 at 12:17

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Peter Heinig, Mark Sapir, Ben Barber, Chris Godsil
If this question can be reworded to fit the rules in the help center, please edit the question.

• FYI: 'tentacle' and 'attachment' are horrible and highly unusual terms; the usual technical term is 'hyperedge', or even shorter, 'edge'. – Peter Heinig Feb 25 '18 at 20:01