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The State of the Art in Multilayer Network Visualization

Mohammad Ghoniem, Fintan Mcgee, Guy Melançon, Benoit Otjacques, Bruno Pinaud

arXiv:1902.06815v1cs.SI

TL;DR

Simple graphs may oversimplify systems composed of interdependent layers, and the multilayer-visualization literature lacked a consolidated state-of-the-art survey. This paper synthesizes visualization approaches, tasks, and techniques across visualization and application domains, identifying open research challenges and future directions.

  • Problem

    The literature lacked a survey consolidating multilayer-network visualization across information visualization and application domains.

    Source: §1 · p. 2

  • Method

    The paper surveys visualization techniques, tasks, tools, and analytic approaches relevant to multilayer networks across visualization and application domains.

    Source: §1 · p. 2, §4 · p. 9

  • Results

    The survey finds existing techniques address many aspects of multilayer visualization, while identifying uncovered task categories and further research needs.

    Source: §5 · p. 21, §6 · p. 24

  • Takeaways & Limitations

    The authors identify closer collaboration with complex-systems and application-domain communities as a route to uncovering and addressing visualization challenges.

    Source: §6 · p. 24

    The survey reports a lack of empirical evaluation for multilayer-network visualizations, with crowdsourcing described as a possible but not assured response.

    Source: §5.6 · p. 23

Abstract

from arXiv · show

Modelling relationships between entities in real-world systems with a simple graph is a standard approach. However, reality is better embraced as several interdependent subsystems (or layers). Recently the concept of a multilayer network model has emerged from the field of complex systems. This model can be applied to a wide range of real-world datasets. Examples of multilayer networks can be found in the domains of life sciences, sociology, digital humanities and more. Within the domain of graph visualization there are many systems which visualize datasets having many characteristics of multilayer graphs. This report provides a state of the art and a structured analysis of contemporary multilayer network visualization, not only for researchers in visualization, but also for those who aim to visualize multilayer networks in the domain of complex systems, as well as those developing systems across application domains. We have explored the visualization literature to survey visualization techniques suitable for multilayer graph visualization, as well as tools, tasks, and analytic techniques from within application domains. This report also identifies the outstanding challenges for multilayer graph visualization and suggests future research directions for addressing them.

1 Introduction

The paper frames multilayer networks as a way to represent interdependent subsystems that simple graphs may oversimplify. It surveys visualization approaches across information visualization and application domains, then identifies open challenges and future research directions.

1 Introduction

  • Simple graphs can oversimplify real-world systems better represented as interdependent layers, motivating multilayer networks across many research fields.The paper notes examples in life sciences, epidemiology, sociology, digital humanities, and civil infrastructure.Source: §1 · pp. 1–2
  • Visualization systems often address multilayer-like data under varied names, including multiplex, heterogeneous, multimodal, and interdependent networks.The paper treats these as types of data encompassed by Kivelä et al.’s multilayer-network definition.Source: §1 · p. 2
  • Earlier work had begun consolidating visualization from complex-systems and social-network domains, but no survey had quantified and consolidated the state of the art across fields.The gap spans information visualization and application domains.Source: §1 · p. 2
  • The survey aims to reconcile visualization approaches from information visualization and application domains into a consistent set of techniques for multilayer networks.It also identifies outstanding challenges and provides a roadmap for future research.Source: §1 · p. 2
  • The report presents defining concepts and related models, describes application domains, surveys tasks and visualization techniques, and concludes with challenges and a research roadmap.The survey also covers interaction techniques and evaluation considerations.Source: §1 · p. 2

2 Multilayer Networks and Related Concepts

The section distinguishes multilayer networks from related graph models and explains how layers represent meaningful structure in the system under study. It introduces aspects and illustrates the model across graph types and application domains.

2 Multilayer Networks and Related Concepts

  • Multiplex relationships—many relationships between individuals—have roots in sociology, while multilayer networks have become a focus for visualization research in complex networks.The paper describes the concept as present in Moreno’s sociograms and central to work seeking to simplify multiplex relationships.Source: §2 · p. 2

2.1 Defining concepts

  • A multilayer graph represents node-layer pairs, allowing a node to occur in some layers but not others, with edges classified as intra-layer or inter-layer.The layer concept belongs to the system being modelled, whether grounded in physical reality or defined by the domain under investigation.Source: §2.1 · p. 3

2.2 Aspects

  • Aspects group elementary layers by concepts such as data type, species, pathway, time, or event context; a dataset may use one or multiple aspects.Nodes need not occur on every elementary layer, but must occur on at least one layer of each aspect.Source: §2.2 · pp. 3–4

2.3.1 N-partite Graphs

  • Bipartite graphs are a two-layer multilayer-network case with only inter-layer edges, while n-partite and projected graphs can also inform layer definitions.A projection is appropriate as a layer when it reflects the reality of the system being modelled.Source: §2.3.1 · pp. 4–5

2.3.2 Multivariate Graphs

  • Multivariate attributes can distinguish nodes or edges belonging to different layers, but a layer may lack an a priori definition tied to the modelled system.This differs from multilayer structure grounded in a physical or conceptual reality.Source: §2.3.2 · pp. 5–6

2.3 Related Graph Models

  • Related graph models overlap with multilayer networks, but facets often represent alternative ways to explore one dataset rather than layer interactions and their role in the network as a whole.Attributes in multivariate graphs can distinguish layers, although many such visualizations lack a layer defined by the modelled system’s physical or conceptual reality.Source: §2.3.2 · pp. 5–6

2.3.3 Dynamic Graphs

  • Dynamic network time slices can be treated as layers in a temporal aspect, which may coexist with other aspects.The cited discussion also notes that linking relational timing to tie types can support investigation of social dynamics.Source: §2.3.3 · p. 6

2.4 Application Domains and Data

  • Multilayer-network examples span life sciences, social sciences, digital humanities, and infrastructure, where layers capture distinctions such as omics type, relation, entity, or infrastructure network.The surveyed application examples include cross-omics interactions, species-specific pathway comparisons, and interdependent transportation, energy, and telecommunications networks.Source: §2.4 · pp. 6–7

3 Methodology Followed

The survey organizes papers using categories aligned with a nested visualization-design model and selects literature from visualization venues and application domains. It reviews tasks, data definitions, visualization and interaction approaches, attributes, and evaluation.

3 Methodology Followed

  • The methodology structures the survey around categorizing multilayer-network visualization features and selecting relevant papers across covered domains.The authors describe this section as explaining both the feature categorization and paper selection.Source: §3 · p. 7

3.1 Categorisation

  • The survey’s categorization of the most important features of multilayer network visualization to consider for each paper is built in a manner consistent with Munzner’s nested visualization design process model.Multilayer systems addressing new problems and domains may expose tasks that do not fit existing task taxonomies.Source: §3.1 · p. 8, Tasks and Analysis · p. 8

Tasks and Analysis.

  • The review considers tasks and analytics developed for multilayer systems, including novel visualizations such as [30].It recognizes that new problems and domains may require tasks beyond existing taxonomies.Source: Tasks and Analysis · p. 8

Data Definition.

  • For data definition, the survey records dataset nomenclature, the aspects used to define layers, and data structure.It includes terms such as multiplex and heterogeneous.Source: Data Definition · p. 8
  • The review categorizes visualization approaches, including novel applications of existing approaches, and identifies systems applicable to multilayer networks even when their original sources did not use that label.The text gives as an example of a novel application.Source: Data Definition · p. 8

Attribute visualization:

  • The survey considers interaction across multiple layers and the role of multilayer structure in visualizing multivariate attributes.It notes that multi-layer interaction often requires innovative techniques.Source: Data Definition · p. 8, Attribute visualization · p. 8

Empirical Evaluation:

  • The authors examine whether techniques have been empirically validated for usability, while noting that application-domain techniques may receive less rigorous evaluation.They cite evaluation guidance and identify evaluation as a challenge for information visualization.Source: Empirical Evaluation · p. 8

3.2 Papers Selection

  • Visualization literature was searched in prominent venues using multilayer-related keywords, while application-domain papers were added through citations, reviewer feedback, and author review.The search began with IEEE Xplore and the ACM Digital Library; papers were reviewed by at least one author, with inclusion decisions discussed among co-authors.Source: §3.2 · p. 8

4 Survey of Multilayer Graph Visualizations

The survey organizes multilayer graph visualization around tasks, data definitions, interaction, attributes, and evaluation.

4 Survey of Multilayer Graph Visualizations

  • The survey defines a task taxonomy for multilayer graphs and reviews relevant interaction techniques.It notes that these are considered alongside data definitions, consistently with Munzner’s model.Source: §4 · p. 9
  • The section surveys data definitions and attribute visualization in the context of multilayer networks.These topics are included as components of the structured survey.Source: §4 · p. 9
  • The survey closes its coverage with considerations about visualization evaluation.Evaluation is included alongside tasks, visualization, interaction, and attributes.Source: §4 · p. 9

4.1 Tasks And Analysis

Existing task taxonomies generally do not directly address multilayer networks, so the report proposes task categories centered on layers and surveys related tasks. These range from cross-layer exploration and layer manipulation to comparing layers by numerical or topological features.

Existing task taxonomies

  • Although existing taxonomies cover general, multivariate, dynamic, or domain-specific network tasks, they could be adapted to multilayer visualization.The report focuses on tasks involving visualization rather than tasks addressable only through computation.Source: §4.1 · pp. 9–10

Task category A — Cross layer entity connectivity

  • Cross-layer connectivity tasks explore paths traversing multiple layers, including how shortest paths expand and which nodes they include.Refinery’s associative browsing and Detangler’s leapfrogging illustrate this category.Source: §4.1 · p. 10

Task category B — Cross layer entity comparison

  • Cross-layer entity comparison queries the same or linked entities across layers, as in Jigsaw and FacetAtlas.The compared entities may be the same set of nodes across layers or distinct nodes linked between layers.Source: §4.1 · p. 10

Task category C — Layer manipulation, reconfiguration

  • Layer manipulation tasks split, merge, clone, project, or regroup layers to reveal relationships and offer new perspectives on the data.Examples include drag-and-drop layer combination and g-Miner’s grouping edits.Source: §4.1 · p. 10

Task category D1 — Numerical attributes

  • Numerical layer comparison uses measures summarizing layer content or structure, such as node-degree distributions or inter-layer node disparity.OntoVis supports disparity-based comparison, while Pretorius et al. describe multi-attribute comparison.Source: §4.1 · p. 11

Task category D2 — Topological and connectivity patterns

  • Topological layer comparison examines features such as group structure, hierarchy, scale-free structure, and layer interaction rather than numerical summaries.Examples include Vehlow et al. and tasks R5 and R12 in GraphDice.Source: §4.1 · p. 11

4.2 Data Definition

Visualization research uses several data definitions for networks with multilayer characteristics, but only a few approaches explicitly identify multilayer structure. The report describes explicit layer models alongside systems that imply or infer layers through facets, data sources, or other representations.

Explicit and implicit layer definitions

  • Only a few visualization approaches explicitly mention multilayer networks; many multivariate-network systems combine relational data with node and edge attributes without specifying layers.Some use table-based representations.Source: §4.2 · p. 11

Facets and attribute products

  • Facets in FacetAtlas [21] map naturally to node layers, while Pretorius et al. define nodes as Cartesian products of attributes without using the term layers.Source: §4.2 · p. 11

Inferred and query-based structures

  • Some systems infer multilayer structure by aggregating databases, ego networks, or personal data; others use multiplex or hypergraph representations for query graphs.Source: §4.2 · p. 11

Explicit layer models

  • MuxViz [30] follows Kivelä et al.’s definition, while Detangler explicitly encodes layers to support inter-layer correlation exploration.Layer distinctions such as structural versus functional may also suit different goals.Source: §4.2 · p. 11

4.3 Visualization Approaches

The survey organizes multilayer visualization by how layers are encoded and reviews one-dimensional, node-link, matrix, and hybrid designs. Across these approaches, designs trade explicit layer structure and comparison support against edge clutter, navigation, or other representational constraints.

4.3 Visualization Approaches

  • The survey groups visualization approaches by explicit layer encoding and also notes weaker cues such as node or link colour.Layers may be treated and manipulated as visual objects, or indicated less directly through colour.Source: §4.3 · p. 11

4.3.1 1-Dimensional Representations of Layers

  • One-dimensional designs use circles, arcs, parallel axes, or radial axes to organize layers and support tasks including path tracing and layer comparison.Examples include concentric rings for cross-layer attributes, chord diagrams for shared nodes, parallel axes for paths, and hive plots for connectivity patterns.Source: §4.3.1 · pp. 13–14

4.3.2 2D, 2.5D and 3D Node-Link Representations

  • Node-link designs commonly encode layers with node colour or shape, but layer relationships remain mixed, nodes intertwine in standard 2D layouts, and edge clutter can make layer-related tasks difficult.The 2.5D approach uses translucent parallel 2D planes to separate within-layer from between-layer links, supporting path-related tasks more naturally than traditional 2D node-link layouts, but requires 3D navigation to change perspective and resolve occlusion.Source: §4.3.2 · pp. 14–15

4.3.3 Matrix-Based Visualizations

  • Matrix views avoid node-link edge clutter and can improve readability for large or dense graphs, though they are less suited to path finding.Row and column ordering affects pattern detection; seriation can arrange links into dense rectangular blocks.Source: §4.3.3 · pp. 16–17

4.3.4 Hybrid Approaches

  • Hybrid approaches combine representations to use their complementary strengths, including node-link and matrix views or multiple coordinated representations.Examples include locally dense network analysis with NodeTrix and cross-view links with VisLink.Source: §4.3.4 · pp. 17–18

4.4 Interaction Approaches

The section distinguishes interaction with individual network elements from interaction with whole layers or layer groups. It describes layer reconfiguration, comparison, and coordinated selection across representations.

Layer-level interaction

  • Layer-level interaction needs a visual affordance and can operate on individual layers or groups of layers.Donatien supports reconfigure and explore interactions.Source: §4.4 · p. 18

Layer organization and comparison

  • Donatien supports small multiples, stacked layers, and animation, with dragging, reordering, layout changes, and crossing-based flipbook comparison.Its stacked view also groups spatially close nodes across layers, and lets analysts edit or merge those clusters.Source: §4.4 · p. 18

Hierarchical layer organization

  • Hierarchies can organize layers so that collapsing or expanding a parent corresponds to merging or splitting its child layers.OntoVis uses an ontology visualization to steer the associated network visualization.Source: §4.4 · p. 18

Coordinated views

  • Detangler coordinates a network-connectivity view with a separate view of layer interactions.Its paired panels display node connectivity and how layers interact, with interaction defined in a domain-dependent manner.Source: §4.4 · p. 18

Coordinated selection

  • Detangler’s leapfrogging links node and layer selections, expanding selections by Boolean OR or restricting them by Boolean AND.Selecting layers can identify nodes involved in any selected layer or only nodes involved in all selected layers.Source: §4.4 · p. 19

4.5 Attribute visualization

Attribute visualization addresses values that vary across nodes and layers, using both separate attribute views and encodings integrated with network structure. The reviewed approaches include per-layer comparison, aggregation, and coordinated interaction.

Attributes across layers

  • Node attributes, especially graph-derived metrics, can vary across layers and be shown with rings representing layers or centralities.MuxViz uses annular rings to display metric values across layers.Source: §4.5 · p. 19, Figure 10 · p. 20

Linking attributes and structure

  • Attributes may be integrated into network views or coordinated with them through linked brushing that highlights related nodes.The section also describes parallel coordinates and heat maps adapted to compare attributes across layers.Source: §4.5 · p. 19, Figure 11 · p. 20

Task-dependent attribute views

  • The suitable attribute view depends on the task; SPLOS orders pairwise scatterplots by correlation and uses common axes to compare attributes across layers.The section presents this as potentially more efficient in comprehension and space than a scatter-plot matrix for that goal.Source: §4.5 · p. 20

Interactive attributes

  • Attribute visualization can be coupled with interaction: Detangler colours a selection lasso to represent the selected nodes’ level of entanglement.Entanglement is described as measuring a group’s internal cohesion.Source: §4.5 · p. 20

Aggregated attributes

  • Attribute summaries can aggregate networks or layers for characterization and comparison, as in GraphTrail and ManyNets.ManyNets uses bar charts to summarize network attributes and a tabular view to support comparison and sorting.Source: §4.5 · p. 21, Figure 12 · p. 21

4.6 Empirical Evaluation

The survey finds limited low-level empirical evaluation of multilayer visualization. It attributes this partly to the scarcity of defined low-level tasks and comparable techniques, and notes the lack of demonstrated usability gains for 3D graph visualization outside specified viewing conditions.

Evaluation coverage

  • Low-level empirical evaluations specific to multilayer visualization are scarce, alongside a lack of clearly defined tasks and comparison techniques.Novel interactions may not be directly comparable to existing techniques, while some work instead uses feedback, expert review, or usage scenarios.Source: §4.6 · p. 21

3D evaluation

  • Outside stereoscopic viewing or motion and depth cues, empirical studies have not demonstrated usability gains from 3D graph visualization.The survey notes an exception for stereoscopic viewing conditions.Source: §4.6 · p. 21

5 Discussion and Open Challenges

The report finds that existing multilayer visualization techniques offer a starting point, but the model's complexity leaves open needs in task design, layer modelling, visualization, interaction, and evaluation. It identifies research opportunities across these areas.

5 Discussion and Open Challenges

  • Multivariate and faceted visualization do not fully encompass multilayer networks, whose complexity leaves gaps in tasks, layer modelling, visualization, interaction, and empirical evaluation.The report identifies these as open challenges for future work.Source: §5 · p. 21

5.1 Multilayer Networks Task Taxonomy

  • Layer-related tasks are fundamental to multilayer graph task taxonomies, alongside node- and edge-related tasks, although existing taxonomies can still apply within individual layers.Graph comparison is not covered by Lee et al.'s taxonomy.Source: §5.1 · pp. 21–22

5.2 Data Definition

  • Choosing which aspects constitute layers is an early design concern, and real-world data often require substantial work to become multilayer datasets.Reviewed visualization papers often start with cleaned data, while application-domain work may focus on generating multilayer datasets [42].Source: §5.2 · p. 22, Modelling of real world concepts from… · p. 22

Modelling of real world concepts from the data

  • Layer definitions can use combined node attributes or edge types, while clustering, projection, and degree-of-interest functions offer analytical ways to generate or select layers.For example, clustering may reveal geography in a predator–prey network, and projecting an author–paper network onto papers yields co-authorship links between researchers.Source: Modelling of real world concepts from… · p. 22

5.3 Visualization approaches

  • Only a small subset of visualization approaches has been hybridized; edge routing, temporal integration, and representing hyper-edges across discrete layers remain open opportunities or challenges.The report intentionally excludes hypergraphs, despite their use in applications such as biological pathways.Source: §5.3 · pp. 22–23

5.4 Interaction Approaches

  • Existing systems offer some multilayer interaction support, but inter-layer exploration and layer creation or manipulation still have substantial design space.Detangler supports task categories A, C, and D; Donatien supports layer comparison and defining layers for comparison.Source: §5.4 · p. 23

5.5 Attribute visualization

  • Multilayer attribute visualization could better integrate centralities with network structure to support cross-layer comparison of attributes and structure.The report notes that many existing attribute techniques can be adapted, while Detangler's multilayer metric is a more novel example.Source: §5.5 · p. 23

5.6 Evaluation

  • Empirical evaluation is lacking, and crowdsourcing may help, but complex tasks, datasets, and limited support for highly interactive studies make evaluation challenging.New academic-driven platforms may simplify evaluation of more complex tasks.Source: §5.6 · pp. 23–24

6 Conclusion and Roadmap for Future Research

The report surveys multilayer network visualization across visualization and application domains, finding many techniques that address different aspects of the problem. It identifies further research needs and calls for closer collaboration with application and complex-systems communities.

6 Conclusion and Roadmap for Future Research

  • The survey consolidates the state of multilayer network visualization across visualization and other domains, finding techniques that address many aspects of the problem.Source: §6 · p. 24
  • Reframing user needs and data as multilayer problems may expose commonalities across terminology and connect visualization researchers with application-domain researchers.Source: §6 · p. 24
  • Closer work with application domains can refine multilayer task descriptions and clarify shared problem elements and available solutions.The report recommends consolidating and refining tasks with the typology of Munzner and Brehmer.Source: §6 · p. 24
  • Closer interaction with complex-systems researchers may bring underused multilayer analytics into visualization and help address application-domain challenges.Source: §6 · p. 24
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