Alluvial Charts and Their Discontents

The Sankey diagram is increasingly popular for data visualization. Like all network diagrams, a sankey diagram represents explicit connections between elements. It represents an explicit system, rather than a simple collection of correlated datapoints.

But their sophisticated visual rhetoric poses difficulties for information designers familiar with bar and line charts. At Netflix I built a complicated interface for tracking user flow that leverages sankey diagrams, and learned a few things about how to utilize them.

Why sankey?

Both designers and readers are drawn to system visualization forms like sankey diagrams. Sankey diagrams, more than other network diagrams, are so powerful because they show flow. “Follow the money”, Deep Throat says in All the President’s Men, not “plot the correlation of campaign contributions and influence”. Flow — of traffic, of goods, of people, of money — is one of the key ways in which we organize our world.

Plus, because they visually resemble rivers, they are a sensible and familiar visual metaphor, much like the pie chart showing the amount of pie eaten.

The original sankey diagram, created by Matthew Henry Phineas Riall Sankey in 1898, was a comparison of idealized to actual flow of energy in a steam engine. It allows readers to quickly scan a very complex system and see how a particular implementation, in this case the plant at Louisville Leavitt, differs from an idealized steam engine design.

Interestingly, the historical inspiration for generic sankey layouts differs in one key aspect: It is cyclical. Modern implementations, such as d3-sankey, require what are known as directed acyclic graphs (DAGs). While it’s an intimidating term, a DAG simply refers to a network (or graph) that has direction (the connections indicate something moving from a source to a target) and has no loops or cyclics (the meaning of ‘acyclic’). So, the Louisville Leavitt dataset and the idealized steam plant dataset, both of which return water back into the system, would crash d3-sankey, which expects no feedback loops. Almost all sankey diagrams in use today are of this variety of limited sankey that doesn’t allow for feedback.

Paths as flows

While sankey diagrams are designed to visualize flow, often they are used to visualize paths. To really see the difference between paths and flows, let’s look at a word tree from Jason Davies’ contrasted with a diagram of a watershed.

As you can see, the sentences in the word tree can branch but never rejoin, unlike the river system which does so throughout. Once a path branches from another path, you lose the memory of that individual path through joining. Path memory simply refers to the ability to reconstruct the exact steps in a path, which can still be done in a hierarchical layout like the dendrogram used by Jason Davies but cannot be done in a sankey diagram. It’s through aggregation of individual paths that we get to datasets used to visualize flow, such as visit flow in web sites. This aggregation is done by creating bigrams out of the paths, and then weighting the bigrams.

This isn’t an academic distinction. When you build a sankey diagram from paths, as I did at Netflix showing the different paths a user navigates through the site, then readers will see flows and want the diagram to be able to also show them paths. Any flow diagram that was built from path aggregation needs to maintain path memory, even though the data structure of the sankey diagram only cares about those memoryless bigrams.

Sankey issues

Despite their attractiveness, sankey diagrams are difficult to implement because of their visual complexity. People simply aren’t as familiar with network data visualization as they are with line charts and bar charts. Data-driven sankey diagrams are laid out automatically, maximizing space, which means that a slight difference between data may lead to nodes or paths being in very different positions. As such, you need to provide interactive and comparative context to readers.

To address this need for context, my own implementation at Netflix included rich interactivity to interrogate and filter the diagram. It also provides a small multiples view that allows you to cross-highlight different filtered versions of a dataset. These features familiarize a reader with a sankey diagram’s dynamic layout and allow for comparison of patterns by interactively highlighting the shared structures within and between the diagrams.

You’ll notice that this implementation doesn’t utilize color to encode categories or quantities. That was a decision based on the complexity of the diagram and my desire not to overwhelm a user with too many channels. You’re already asking for significant investment when you present a chart where size and position do not correspond to the typical datapoints that a reader expects.

The future of sankey diagrams

As network data visualizations become more familiar to audiences, and the sankey diagram in particular, we should expect to see an uptick in its deployment as well as more sophisticated versions of the diagram. There are already examples of off-the-shelf BI tools that feature sankey diagrams, as well as open source projects that provide sankey diagrams as one of the options. The sankey diagram is one of the most readable of the complex data visualization methods but despite this there seems to be little effort to produce more than the traditional Limited Sankey layout. What’s really needed is a layout that produces the cyclical representation present in Sankey’s original diagram.

As with most data visualization layouts, the real work to be done isn’t in more sophisticated graphical representation, but rather better UI/UX and integration into truly useful charts and interfaces. Sankey diagrams are very hard to read, and a poor interface around it is just going to increase that cognitive load, and require too much investment from your readers.

This piece originally appeared on my personal site back in 2015, where you could never discover it because I’m a terrible webmaster.

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