# Mapping change in higher-order networks with multilevel and overlapping communities

## TL;DR

This paper extends alluvial diagrams to visualize community changes in higher-order networks with layered, overlapping, and multilevel structures, providing an interactive tool for better understanding complex network dynamics.

## Contribution

It generalizes alluvial diagrams for higher-order networks, enabling visualization of multilevel and overlapping community changes, and offers an interactive tool for researchers.

## Key findings

- Visualized the effect of memory in citation networks.
- Distinguished multidisciplinary from field-specific journals.
- Enhanced understanding of higher-order network dynamics.

## Abstract

New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial generator to illustrate the effect of modeling network flows with memory in a citation network, distinguishing multidisciplinary from field-specific journals.