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Hypergraph

As explained in Graph Neural Networks in Action

A hypergraph is a graph in which a single hyperedge can connect any number of nodes rather than exactly two.

A hypergraph extends an ordinary graph by allowing one hyperedge to connect any number of nodes. Use it when a relationship naturally involves a group rather than a pair. section 1.2.2

Key implementation-facing distinctions:

  • Ordinary graph edges connect exactly two nodes, while hyperedges may connect multiple nodes or represent a self-loop. section 1.2.2
  • Connectivity uses an incidence tensor rather than a two-dimensional adjacency matrix; its dimensionality reflects the maximum nodes joined by one hyperedge. section 1.2.2

Group communication

Represent a communication platform with one hyperedge joining every participant in a group chat; pairwise conversations remain ordinary two-node edges. section 1.2.2

How Graph Neural Networks in Action covers it

How deep it goes
Defines hyperedges and incidence tensors, but stops short of algorithms or implementation code.
Examples
Uses group chats, isolated nodes, self-loops, and hyperedges joining up to three nodes.
What it assumes
Assumes basic graph terminology and contrasts hypergraphs with ordinary graphs.
What you can do after
Evaluate whether a relationship requires multi-node edges rather than ordinary pairwise graph connections.
How it connects
Contrasts ordinary graphs and connects graph connectivity with adjacency matrices and incidence tensors.
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