Source-linked AI summary
MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
Manlio De Domenico, Mason A. Porter, Alex Arenas
TL;DR
Existing network representations can discard multilayer information and produce misleading results, creating a need for tools that analyze and visualize multiple relationship types. The paper presents muxViz, an open-source methodology and software framework with multilayer algorithms and visualizations. It demonstrates the framework on genetic, neuronal, transportation, and other empirical networks, while using interlayer edge weight 1 as an illustrative choice whose general selection remains open.
Problem
Aggregating multilayer information into single-layer networks can produce misleading results, while biological multilayer analysis lacks sufficient software and multiplexity-aware diagnostics.
Method
The paper develops muxViz, an open-source methodology and software framework for analyzing and visualizing multilayer networks through multiple representations, diagnostics, and visualizations.
Results
MuxViz analyzes and interactively visualizes empirical genetic, neuronal, transportation, and geographically embedded multilayer networks, including centrality and interlayer-correlation diagnostics.
Takeaways & Limitations
MuxViz provides a modular open-source framework that helps retain multilayer structure while supporting compact visualization and the addition of new analysis methods.
Takeaways & Limitations
The paper uses interlayer edge weights of 1 for illustration, while choosing appropriate weights remains an open research question.
Abstract
from arXiv · showhide
Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyze and interactively visualize multilayer data using empirical genetic, neuronal, and transportation networks. Our software is available at https://github.com/manlius/muxViz.
1 Introduction
Standard network representations often aggregate multilayer information into a single connection type, risking misleading results. Multilayer networks preserve simultaneous relationships and support richer analyses, but require better tools for visualization, analysis, and interpretation.
- The need for multilayer representations: Aggregating multilayer information into ordinary networks can produce misleading results by retaining only one connection type between entity pairs.The standard network paradigm focuses on connectivity but omits multiple relationship types.
- The need for multilayer representations: Multilayer networks represent entities, relationships, and interaction weights across layers, including entities that participate in multiple relationships simultaneously.This framework encodes richer information than analyzing individual layers separately.
- Existing capabilities: Multilayer analyses have revealed community structure, important nodes, and correlations between nodes in complex systems.Related work spans interdependencies, multilayer structures, dynamics, and control.
- Open challenges: Key challenges are visualizing, analyzing, and interpreting multilayer data, especially because biological applications have used multilayer analysis relatively rarely.The paper attributes this situation partly to a lack of appropriate software.
- Open challenges: Biological multilayer data would benefit from methods and diagnostics that exploit multiplexity, meaning multiple ways for entities to interact.The motivation is especially relevant when overlap between networks indicates correlation but does not exploit the full multiplex structure.
2 Methods
muxViz provides methods and software for visualizing, analyzing, compressing, and interpreting multilayer networks. It supports multiple network representations and diagnostics, including spatial layouts, layer reducibility, and annular comparisons of centrality patterns.
- Software scope: muxViz addresses multilayer analysis and visualization through a practical methodology and accompanying open-source software.The software is modular and includes technical details in Appendix A.
- Visualization: Multilayer networks can be visualized either with explicit layers or as edge-colored multigraphs, while replicated nodes connect across layers through interlayer edges.The paper illustrates both representations using genetic and neuronal networks.
- Visualization: MuxViz focuses on multiplex networks and distinguishes ordinal interlayer connectivity between adjacent layers from categorical connectivity across every layer pair.Ordinal layers follow a criterion such as temporal ordering; categorical layers connect replica nodes from every pair of layers.
- Visualization: The paper illustrates geographically embedded multilayer networks using European airline layers and Ivory Coast mobility and communication layers.MuxViz accounts for spatial information in these visualizations.
- Compression and reducibility: MuxViz can compress layers by estimating pairwise quantum Jensen–Shannon divergences and clustering the resulting distances into a reducibility dendrogram.This implements an information-theoretic tradeoff between accuracy and complexity while allowing alternative layer-reduction methods.
- Annular visualization: The annular visualization represents each information array as a ring, with angle encoding node identity and ring order optimized for readability.It can compare centralities across layers, multilayer networks, and aggregated networks.
3 Analyses of empirical multilayer networks
muxViz demonstrates multilayer analysis and visualization across genetic-interaction, connectome, and other biological networks. Its analyses compare multilayer representations with layer-specific and aggregated-network views using communities, centrality, correlations, compressibility, and interactive visualizations.
- The examples cover Xenopus laevis, Caenorhabditis elegans, Herpes simplex, and HIV-1 multilayer biological networks.
- Multilayer community detection incorporates intralayer and interlayer edges to identify densely connected node sets against a multilayer null model.
- muxViz calculates multilayer and layer-specific centralities, including degree, eigenvector, hub and authority, PageRank, and Katz measures.
- Correlation panels measure mean edge overlap and degree-degree Pearson and Spearman correlations between layers.
- The annular visualizations reveal that physical association and direct interaction dominate multilayer strength, while some multilayer rankings poorly correlate with aggregated or layer-specific rankings.
- The analyses compare multilayer diagnostics with aggregated-network and individual-layer results, including community assignments and PageRank rankings.
- Additional views include edge-colored multigraphs, layer compressibility and reducibility dendrograms, and rings representing centrality descriptors across layers and network aggregations.
4 Conclusion
The conclusion presents muxViz as open-source software and methodology for exploiting multilayer structure in increasingly abundant multilayer data. It emphasizes extensibility and applicability beyond the biological examples.
- muxViz provides an open-source framework and methodology for analyzing and visualizing multilayer networks without discarding important multilayer information.
- Its modular structure and open-source license make it easy to add new methods.
- Although demonstrated on biological networks, muxViz is also useful for multilayer networks in other settings and can overlay analyses on spatial information.
A Technical Details About muxViz
muxViz combines an accessible interface with R and Octave components for multilayer-network visualization and computation. Its modular design supports interactive use and user extensions.
- muxViz uses R for its graphical user interface and Octave for matrix and tensor calculations.
- The software supports local client-side use or access through a remote Web server.
- Users can perform computations and visualizations through the interface without programming skills, while adding modules for new diagnostics and visual representations.
- Two-dimensional and interactive three-dimensional visualizations are supported through OpenGL.