# What is the difference between symmetric bipartite graphs and a complete bipartite graph?

I am studying Restricted Boltzmann Machines (RBMs), and it is described as a symmetrical bipartite graph. Link

How is this different from a Complete bipartite graph? They seem to be the same to me, which is why I'm curious to why there is such a clear difference in terminology.

## 3 Answers

Your first link's usage of 'symmetrical bipartite graph' is indeed puzzling. From my knowledge of RBMs it would have been better for them to say 'complete bipartite graph' as you suggest.

The only formal reference I can find online for 'symmetry' in bipartite graphs is this link. But that does little to explain the usage in your case.

From the link you provide the say the definition of those terms is:

Symmetrical means that each visible node is connected with each hidden node (see below). Bipartite means it has two parts, or layers, and the graph is a mathematical term for a web of nodes.

I would say that symmetrical is just their definition and that nodes are separated into two partitions: in one partition are visible nodes and in the other partition are the hidden nodes.

So I wouldn't pay much attention to it ...

in some contexts a symmetric graph G may be a graph which admits a non-trivial graph isomorphism (vertices and edges) to itself, perhaps with some additional requirements like taking a certain pair u,v to v,u.