# Hierarchical Edge Bundling Explained (3/3)

In this post, I will go over the related works of hierarchical edge bundling mentioned in D. Holten’s 2006 paper.

Note that this post is not about the hierarchical edge bundling itself. If you want to know about it, please visit the first post of this series.

# Confluent Drawing

As mentioned in the previous post, the idea of edge bundling was not first proposed in Holten’s paper. Another visualization method, proposed by Eppstein and others, is known as *confluent drawing*.

Confluent drawing was originally proposed and studied as a method to depict non-planar graphs in a way that avoids edge crossings. This might seem confusing because, by definition, non-planar graphs inevitably have edge crossings. Let’s first take a look at an example.

The complete bipartite graph, composed of three vertices on each side, is not a planar graph (the left figure). A corresponding confluent drawing is shown on the right. You might say “hey, edges are crossing!”

The key lies in the definition of “crossing.” In confluent drawing, smoothly connected (locally-monotone) curves are not considered as crossing. A graph is defined as *confluent* when it can be drawn solely with edges that are smoothly connected, although not all graphs are confluent.