nVenn2: faster, simpler generalized quasi-proportional Venn diagrams
Samuel Pis-Vigil, María González-Pereira, Magda R. Hamczyk, Vı́ctor Quesada · 2026 · 1 citationsRead the paper
Abstract Motivation: Proportional Venn diagrams provide a compact representation of the relationships between sets. Each relationship is represented with a region whose area reflects the number of elements shared by a given combination of sets. This means that the number of regions grows exponentially with the number of sets, which is why proportional Venn diagrams with more than five sets are cumbersome to interpret and seldom used. However, Venn diagrams with a large number of sets may still be legible if enough regions are empty and do not need to be represented. Results: Here, we present nVenn2, the second version of the nVenn algorithm, to create quasi-proportional Venn diagrams. This new version uses a different, more flexible approach which includes steps to minimize the complexity of the diagram. Thus, computation time for nVenn2 mainly grows with the number of non-empty diagram regions, rather than with the number of sets. This property allows users to create interpretable quasi-proportional Venn diagrams with large numbers of sets. Availability and implementation: The nVenn2 algorithm is freely available as an executable program, as a web page, as an R package (nVennR2) and as a Python package (nVennPy). All interfaces allow users to edit the appearance of the resulting diagram.
What the full text shows
Working prototype- nVenn2 enables the creation of interpretable quasi-proportional Venn diagrams with more than nine sets, which was not feasible with the previous nVenn version. (When enough regions are empty and do not need to be represented)
- Computation time for nVenn2 scales primarily with the number of non-empty regions rather than the total number of sets.
- nVenn2 is consistently faster than nVenn for diagrams containing six or more sets. (Compared to nVennR)
- The algorithm maintains area proportionality for regions, though a minimum radius constraint exists. — radius >= 2% of diagram width
- Setup
- Benchmarking used 40 independent diagrams per combination of universe sizes (20, 30, 50 elements) and varying numbers of sets.
- How
- The algorithm uses a seven-step process involving a simulation with dissipative friction and spring-like forces to position circles representing regions, followed by the generation of set lines. It employs gradient descent and region-swapping to minimize compactness and the number of line crossings.
- Limitations
- The radius of any circle cannot be less than 2% of the diagram width, potentially misrepresenting very small regions. · The algorithm may stop at a local minimum in complex cases, requiring multiple runs or a computationally expensive global minima search. · The procedure to find global minima can require large computational resources and running time. · The topological generation step can fail in particularly complex cases, though error frequency is reported as exceedingly low.
Summarized by Gemma 4 from the open-access full text · 11 Oct 2026. Read it