Backflow and loops disqualify the Sankey

What it is

A conventional layered Sankey orders nodes into stages and sends bands along one primary direction. Backflow or a cycle returns to an earlier stage, undermining that directional reading and low-crossing layout. “Disqualify” in the title therefore applies to the conventional directed-acyclic form, not to every mathematical representation of cyclic flow. Time unfolding, an explicitly routed circular Sankey, a network, a chord diagram, or a state-transition view may work depending on whether readers need net flow, gross exchange, cycle count, or path sequence.

Why it happens

In an acyclic layout, layer position encodes stage order while band direction encodes transfer. A back edge must route around existing layers or cross forward bands, adding length, intersections, and endpoint ambiguity. The same unit can also traverse a cyclic node repeatedly. Width that counts passages is no longer the number of distinct entities, though it may remain a valid gross event flow. A cycle does not inherently violate conservation; trouble arises when time window, counting unit, and repeated-passage semantics are hidden and readers conflate stock, entities, and events.

Studying it

Derive entity paths, transition events, net flow, and gross flow separately from logs, then compare time-unfolded Sankeys, circular Sankeys with back edges, chord diagrams, adjacency matrices, and sequence views. Test backflow-source lookup, circulation strength, entity tracing, net-versus-gross comparison, and stage localization. Measure errors, time, backtracking, and counting-semantic misunderstandings while varying cycle count, span, repetition, crossings, and time resolution. Every graphical answer should be reproducible from events; attractive layout alone does not establish suitability.

Where it stops holding

A small number of important, directly labelled backflows can supplement a main Sankey with outside return bands, provided the display no longer pretends to be purely left-to-right. Netting bidirectional flows answers a balance question but erases large opposing exchanges, circulation, and exposure; use it only for a genuinely net task. Time unfolding removes graph-theoretic cycles at the cost of repeated nodes and horizontal length. When cycles are the primary structure of a state machine or network, forcing stages is often weaker than a dedicated cyclic representation.

Applying it

• Detect self-loops, back edges, and strongly connected components during modelling. State whether width means entities, transition events, money or material, net flow, or gross flow.
• Use net flow for net-balance tasks while exposing gross or cancelled amounts; unfold time for paths; reserve outside return bands for sparse backflow; switch to networks, matrices, or chords for cycle structure.
• Directly label return direction, value, interval, and repeat-count rule, and provide a keyboard-accessible transition table and screen-reader path summary.
• Validate with large opposing flows whose net is near zero. If readers miss gross circulation or interpret passage counts as distinct entities, change the definition or chart.

Related

• Same group: U2.12.1 Sankey diagrams encode conserved flows as band width · U2.12.2 Node ordering and crossing count decide readability · U2.12.3 With huge magnitude gaps, small flows vanish · U2.12.5 Band width is a length encoding; one scale for the whole diagram
• Nearby: U2.13.2 Layout algorithms shape node-link readings · U2.14.1 Parallel coordinates render each record as a polyline across axes
• Search terms: circular Sankey · backflow · cycle detection · gross versus net flow · time unfolding