Vertices connected by an edge are said to be adjacent.

An edge connects these two vertices through the center of the projection.

There is, at present, no way to represent the length of an edge connecting vertices.

Thus, the edges connecting communities will have high edge betweenness (at least one of them).

It saves which vertices of the graph are connected by an edge.

Two vertices are connected by an edge whenever one set is a subset of the other.

In particular, two generators commute if and only if they are not connected by an edge.

Every vertex pair is connected by an edge, except opposites.

And the edges only connect nodes of different types.

A common extension is to hypergraphs, where an edge can connect more than two vertices.