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8JOURNAL OF LATEX CLASS FILES, VOL. 1, NO. 1, JANUARY 2016 1

Towards Faithful Graph VisualizationsQuan Hoang Nguyen, Peter Eades

Abstract—Readability criteria have been studied as a measurement of the quality of graph visualizations. This paper argues that

readability criteria are necessary but not sufficient. We propose a new kind of criteria, namely faithfulness, to evaluate the quality

of graph layouts. Specifically, we introduce a general model for quantifying faithfulness, and contrast it with the well established

readability criteria. We show examples of common visualization techniques, such as multidimensional scaling, edge bundling

and several other visualization metaphors for the study of faithfulness.

Index Terms—faithfulness, faithful graph visualization, information faithful, task faithful, change faithful.

✦

1 INTRODUCTION

V ISUALIZATION aids visual acuities for patterndetection and knowledge discovery by enabling

transformation or deduction from information toknowledge through visual means. Visualization hasbeen widely used for illustrating, formulating hypoth-esis, identifying patterns, constructing knowledge,performing tasks and making decisions.

Technological advances have dramatically increasedthe volume of network data. Graphs generated inmodern applications become larger and more com-plex. Since then, graph visualization techniques aregetting more sophisticated and involving complex pa-rameter settings to turn graphs into drawings. Thus, itis vital to justify how reliable visualizations methodsand models are.

“Readable” pictures of graphs are the common aimthat has been addressed in graph drawing algorithmsdeveloped over the past 35 years. Here “readability”is measured by aesthetic criteria, such as:

1) Crossings: the picture should have few edge cross-ings.

2) Bends: the picture should have few edge bends.3) Area: the area of a grid drawing should be small.Readability criteria have been extensively studied in

numerous visualization systems [72], [75]. Algorithmsthat attempt to optimise aesthetic criteria have beensuccessfully embedded in systems for analysis in awide variety of domains, from the finance industry tobiotechnology.

In this paper, we argue that readability criteria forvisualizing graphs, though necessary, are not suffi-cient for effective graph visualization.

Traditionally, it is quite commonplace for the “pre-sumption” that quality of visualization is measured bythe readability of the visualization; see [65], [68], [72],[75]. Such readability criteria presumes that readabil-ity implies that the picture is a faithful representation

• Q. Nguyen and P. Eades are with the School of Information Technolo-gies, University of Sydney, Australia.E-mail: {quan.nguyen,peter.eades}@sydney.edu.au

(a) Original graph (b) Edge contraction

Fig. 1. An example of edge concentration [59]

(a) Original graph (b) Confluent drawing

Fig. 2. An example of confluent drawing [20]

of the data. For the last couple of decades, traditionalways of visualization of the graphs use node-linkdiagrams to visualize the whole graphs, which arecomprised of a fairly limited number of nodes andedges. Hence, the presumption may be clearly true inthese traditional approaches to graph visualization.

However, for modern visualization metaphors, suchas 2.5D visualizations, map-based visualizations, ma-trix representations and their combinations, the read-ability criteria is not sufficient. Further, the presump-tion can be demonstrably false because of the exten-sive use of clutter reduction techniques, such as edgebundling. For large-scale graphs in modern applica-tions, visualization of the whole graph is not alwaysfeasible. Since data reduction and aggregation becomecommonplace, readability criteria is not sufficient.

Here, we introduce another kind of criterion, gener-ically called “faithfulness”, that we believe is neces-sary in addition to readability. Intuitively, a graphdrawing algorithm is “faithful” if it maps different

http://arxiv.org/abs/1701.00921v2

JOURNAL OF LATEX CLASS FILES, VOL. 1, NO. 1, JANUARY 2016 2

graphs to distinct drawings1. Using mathematicalterms, a faithful graph drawing algorithm encodesan injective function. In other words, a faithful graphdrawing algorithm never maps distinct graphs to thesame drawing.

We show several examples below for illustrating thenew faithfulness criteria.

1.1 Motivating examples

Many graph visualization algorithms have embeddedone or more aesthetic criteria to achieve readable lay-outs. In some cases however, graph layout algorithmscannot avoid visual clutter or edge cluttering dueto high edge density from intrinsic connectivity andoverlapping between nodes and edges.

In such cases, edge concentration [59], confluent draw-ing [14], [19] and edge bundling [27], [37], [81] becomeuseful. These edge routing algorithms share the sameidea: they simplify edge connections in the pictureto increase readability. Such improved readability ishelpful with respect to a number of tasks, yet thepictures may become less faithful.

As an example, edge concentration [59] simplifiesedge connections in the picture to increase readability.Figure 1 shows two pictures of a bipartite graph;Figure 1a is a simple drawing with straight-line edgesand Figure 1b is another drawing with “concentrated”edges. Figure 1b has less edge crossings and is morereadable. However, Figure 1b would also give aviewer, who does not know how the picture wasmade, at the first sight: a graph comprising of tencircle nodes and two boxes connected by twelve lines.This demonstrates the lack of faithfulness of edgeconcentration.

For our second example, Figure 2a shows anotherbipartite graph; the confluent drawing of the graphis depicted in Figure 2b. Confluent drawings may benot faithful. For example, one may find there is no linkconnecting the two red circles in Figure 2a. In contrast,one may see from Figure 2b a curve connecting thetwo red circles. This is clearly an inconsistency in theconfluently drawn graph.

As an example of edge bundling, Figure 3 showstwo pictures of the same graph. Figure 3a is a simplecircular layout with straight-line edges and Figure 3bhas the same node positions but with “bundled”edges.

In the example of edge bundling, bundling oftensacrifices faithfulness. Remarkably, while the visualeffects of bundled edges give a more readable visualrepresentation of the overall graph, the ability tolocate, select or navigate individual edges, hoppingbetween nodes is lost. Even worse, bundling canresult in situation where two different graphs can be

1. In Mathematics, a faithful representation of a group on a vectorspace is a linear representation in which different elements in thegroup are represented by distinct linear mappings.

(a) Unbundled (b) Bundled

Fig. 3. An example graph using force-directed edge

bundling

(a) Unbundled (b) Bundled

Fig. 4. A 10 percent modification of the example graph

in Figure 3(a) and the result using force-directed edgebundling

mapped to the same picture. For example, Figure 4ashows a graph that differs from the graph Figure 3aby almost 10 percent of the total number of edges.This graph is bundled in Figure 4b. The bundledrepresentations of the two different graphs (Figure 3band Figure 4b) are identical.

1.2 Aims and contributions

The examples in previous section have demonstratedthat faithfulness is an important aspect of graph visu-alizations. Yet, faithfulness has yet been paid enoughattention by the visualization community. There are afew notions along the lines of faithfulness in scientificvisualization, such as fidelity of the picture [56], and vi-sual reconstructability for flow visualization [45]. In ad-dition, several formal models have been proposed [9],[10], [50], [67], [78]; they aim for assessing the visual-izations as well as for guiding the future of researchin Information Visualization. Nevertheless, there is nomodel of faithfulness for graph visualization.

In this paper, we distinguish two important con-cepts: the “faithfulness” and the readability of visual-izations of graphs. Faithfulness criteria are especiallyrelevant for modern methods that handle very largeand complex graphs. Information overload from verylarge data sets means that the user can get lost inirrelevant detail, and methods have been developed toincrease readability by decreasing detail in the picture.

With a vast amount of methods and techniques


for visualizing the data sets at various levels ofgranularity, it is important to know how reliable thevisualizations being produced are. This demand hasbecome urgent given the popularity of network data,the information overload from technological advancesand various challenges for visualizing large complexand dynamic networks.

In summary, we make the following contributions:

• General model of graph visualization: In orderto describe the faithfulness concept, we present ageneral model of graph visualization process inSection 3.

• General model of the faithfulness: Here, thefaithfulness concept is divided into three types offaithfulness: information faithfulness, task faith-fulness and change faithfulness.

• Examples of faithfulness metrics: We furtherdefine some examples of the faithfulness metrics,which aim to compare the usefulness / effective-ness of different visualizations. We should em-phasize that these metrics are just the examplesand are not the “only” ones.

• Case studies of faithfulness: As for demon-stration, we use popular visualization methodsincluding force-directed methods, multidimen-sional scaling, matrix representations, and hybridmetaphors to evaluate our faithfulness concept.

The rest of the paper is outlined as follows. Section 3presents our general model of graph visualizationprocess. We use this visualization model to describethe faithfulness concept. Section 4 describes our gen-eral model of the faithfulness of a graph visualizationmethod. Here, we divide the general concept intothree kinds of faithfulness: information faithfulness,task faithfulness, and change faithfulness. Section 5shows our examples of faithfulness metrics, whichare computed for quantifying and comparing thefaithfulness of different visualizations. We illustratefaithfulness with several examples in Sections 6, 7 and8: multidimensional scaling, edge bundling and sev-eral selected visualization metaphors (matrix-basedand map-based visualizations). Section 10 concludesthe paper with a remark about the failure of 3D graphdrawing to make industrial impact.

2 RELATED WORK

2.1 Evaluation of visualization

There have been increasing interests in evaluativeresearch methodologies and empirical work [9], [10],[50], [51], [67], [78].

There are several notions along the lines of faithful-ness in scientific visualization. These include fidelity ofthe picture [56], and visual reconstructability for flowvisualization [45] and faithful “functional visualizationschema” introduced by Tsuyoshi et. al. [71]. This no-tion is to judge the transformation from data schemato visual abstraction schema.

A number of quality metrics have been recentlyproposed for evaluating high-dimensional data visu-alization [4]. A survey of quality concerns for parallelcoordinates is given in [12]. There is also proposalfor judging visualizations regarding the presenceof difficulties and distracting elements (or so-called“chartjunk”) [42]. Other research focuses on narrativevisualization and the effects on interpretations withrespect to the intended story [43].

These previous research on visualization evaluationhas mainly focused on information visualization in abroad sense, while our research addresses the qualityof graph visualizations.

Recently, an algebraic process to evaluate visual-ization design has been proposed [48]. Their notionsof representation invariance, unambiguous data depictionand visual-data correspondence are close to our conceptof information faithfulness and change faithfulness.They evaluated their approach on bar charts andscatterplots. In contrast, our approach aims for thequality (the faithfulness) of graph visualizations.

2.2 Readability in graph visualization

Graph drawing algorithms in the past 30 years typ-ically take into account one or more aesthetic criteriato aim to increase the readability of the drawing andto achieve “nice” drawings. There are a wide rangeof aesthetic criteria proposed for graph visualizations.They include, for example, (1) minimizing the numberof edge crossings minimization [69]; (2) minimizingthe number of bends in polyline edges [69]; (3) in-creasing orthogonality: placing nodes and edges toan orthogonal grid [69]; (4) increasing node distribu-tion [13], [73]. (5) maximizing minimum edge anglesbetween all edges of a node [66]; (6) minimizing thetotal area [73]; (7) maximizing the symmetries in theunderlying network structure [28]; (8) edge lengthsshould be short but not too short [11].

Amongst these aesthetics, minimizing edge cross-ings is the most important criterion from previoususer studies [65].

Optimizing two or more criteria simultaneouslyis an NP-hard problem in general. As such, graphdrawings are often the results of compromise amongseveral aesthetics. Most of previous research has alsoaimed for computational efficiency while achievingthe drawing readability.

In the literature, graph drawing algorithms can begenerally classified, for example, in one the follow-ing criteria: (1) A popular technique is force-directedlayout, which uses physical analogies to achieve anaesthetically pleasing drawing [3], [5], [46]; (2) Severalworks extended force-directed algorithms for drawinglarge graphs in [32], [79]; (3) Multidimensional scalingis another popular method for graph visualizationand visual mining [7]; (4) Another approach takesadvantage of any knowledge on topology (such as


planarity or SPQR decomposition [17], [21], [31], [58],[59]) to optimize the drawing in terms of readability;(5) Other approaches offer representations composedof visual abstractions of clusters to improve readabil-ity.

The faithfulness criterion proposed in this paper isimportant to compare the usefulness of graph visual-izations. This faithfulness is different from readabilitycriteria in the literature.

2.3 Mental map preservation in graph visualiza-

tion

An important criterion for dynamic graph drawingsis mental map preservation [18] or stability [63]. Themental map concept refers to the abstract geometricstructures of a person’s mind while exploring visualinformation. The better the mental map is preserved,the easier the structural change of a graph is under-stood.

To preserve the mental map, some layout adjustmentalgorithms use a notion of proximity and rearrange adrawing in order to improve some aesthetic criteria.These algorithms include, for example, incrementaldrawing of directed acyclic graphs [62], or computingthe layout of a sequence of graphs offline [15], orusing different adjustment strategies in order to com-pute the new layout [41]. Other works have studiedthe mental map preservation while the graph is beingupdated [23], [53], [54]. This can be achieved by usingforce directed layout techniques [23], or by usingsimulated annealing [53].

There are some trade-offs between the readabilityand the stability of (offline) dynamic graph drawingmethods (see a survey by Brandes et al. [6]).

In contrast to the mental map in the previouswork, this paper defines “change faithfulness”, whichcaptures the sensitivity of the pictures to changesin the data. This change faithfulness aims for theunderstanding and evaluation of dynamic graph vi-sualization.

2.4 Temporal and spatial analysis

For analysis of dynamic graphs, it commonly requiresto show the statistical trends and changes over time.Visualization of dynamic graphs also needs to pre-serve user’s mental map [57]. The most commontechniques for representing temporal data are viaanimation and the “small multiples” display (see [2]).The animation approach shows visualizations of thesequence of graphs displayed in consecutive frames.The small multiples display uses multiple charts laidside-by-side and corresponding to consecutive timeperiods or moments in time [1].

Generally speaking, this previous work has beenfocused on the space dimension. For example, most ofthe work considers readability and stability or mentalmap preservation of 2D / 3D drawings of graphs. In

Picture HumanData

dS/dt

dK/dtD L

S

KV

E

P

RT

Task

[ Faithfulness ] [ Readability ]

Fig. 5. Graph visualization model

this paper, we are concerned about the faithfulness inboth the space and the time dimensions.

3 GRAPH VISUALIZATION MODEL

In this section we describe a semi-formal model forgraph visualization. The section first gives basic an-notations of graphs and then describes our graphvisualization model.

A graph G = (N,E) consists a set of nodes N anda set of edges E. Note that, in this paper we use Nto denote the set of nodes and preserve V to denotevisualization. In practice, the nodes and edges mayhave multiple attributes, such as textual labels. Forexample, for Facebook friendship networks, a nodemay be associated with names, education, marriagestatus, current position, etc; whereas an edge mayhave relationship types between two persons. Theseattributes can be important for visualization and anal-ysis. Further, nodes and edges may be timestamped,and the visualization varies over time.

Figure 5 shows our visualization model. It is anextension of the van Wijk model [78]. Our modelencapsulates the whole knowledge discovery process,from data to visualization to human; unlike the vanWijk model, our model includes tasks.

The main processes of the model are “visualization”V , “perception” P , and “task” T , and described asfollows.

3.1 Visualization

The visualization process maps a data item d ∈ D (anattributed graph) to a layout item (sometimes calleda “picture”) ℓ = V (d) ∈ L according to a specifications ∈ S. We write this as follows2:

V : D × S → L, (1)

with data space D, specification space S and layoutspace L

2. For this semi-formal model, we use mathematical notationmore as a concise shorthand rather than a precise description. Forexample, we describe processes as functions, but we should warnthe reader that the domains and ranges of these are sometimes ill-defined.


• The type of data space D to be visualized canvary from a simple list of nodes and edges toa time-varying graph with complex attributeson nodes and edges. There are a vast amountof network data and many of them have beengenerated in fairly high rates.

• The specification space S includes, for example,a specification of the hardware used such asthe size and the resolution of the screen. Thespecification can also include parameter inputsfor visualization, navigation or interaction.

• The layout space L may consist of graph draw-ings in the usual sense, but more generally consistof structured objects in a multidimensional geo-metric space. Sometimes it is convenient to regardthe layout space as the screen; in this case, usingthe language of Computer Graphics, it is an imagespace.

In many applications, nodes and edges of a graphin the data space D may contain several attributes. Forexample, a social network from Facebook have nodesrepresenting people and edges representing their so-cial connections. In this network, nodes (people) mayhave other information such as age, gender, identity,marital status, education, and many more. Edges maybe associated with additional information of whetherthey are classmate, colleague or family relationships.

Typically, to represent different attributes in the lay-out space L, the drawings may comprise of a varietyof visual cues, such as color, shape or transparency.For classic drawing algorithms, the visualization pro-cess may compute the layout directly from the data.

For incremental algorithms, the visualization processmay use the previous layout when computing thecurrent layout. The capability of modelling incre-mental algorithms as well as dynamic graphs makesour visualization model more general than the vanWijk model [78]. In this case, the general form ofvisualization process becomes:

V : D × S × L → L,

where the previous layout is the input for computingthe current layout. This is necessary, for example,when a layout algorithm attempts to preserve theuser’s mental map. However, unless otherwise statedwe take the simpler model in equation (1).

3.2 Perception

The perception process maps a picture from the layoutspace L to the knowledge space K . We write this asfollows:

P : L → K (2)

In this model we use the term knowledge – sometimescalled insight or mental picture – to denote the effecton the human of his/her observation of the picture.

Again, in time-varying situation, the human’s percep-tion can depend on the previous picture, and perhapsit is better to write:

P : L×K → K

However, we use the simpler model (2) unless other-wise stated.

Of course, it is difficult to formally model humanknowledge or insight, and it is difficult to assessits value [61]. In particular, in some situations suchas exploratory visualization, the information that iscontained in the data is not known a priori, and wemake pictures to get serendipitous insight. This is awell-known paradox; we do not know in advance theaspects or features that should be visible and thus itis hard to assess how successful we are.

In terms of perception, the human perceptual sys-tem has several constraints. Some visual channels areprobably more representational, expressive or perceiv-able than others. For instance, size and length aremore effective for quantitative data. Yet, for ordinal ornominal data, size and length are less useful. In otherexample, one person can distinguish some pairs /groups of colors more easily than other persons can.Sometimes, the effectiveness of a visual channel mayvary between people; different people may perceive apicture differently.

3.3 Task

Visualizations are a useful means for exploration andexamination of data using visual representations orpictures. In many practical cases, visualizations aredeveloped to serve for domain-specific tasks [76].Examples of common tasks include, for example,identifying important actors and communities in asocial network, or exploring possible pathways in abiological network. To understand faithfulness, it isimportant to model these tasks.

Generally speaking, tasks can be distinguished as“low-level” tasks [80] and “high level” tasks [36]. Forexample, Wehrend and Lewis [80] gives a list of pos-sible low-level tasks (e.g., identify, locate, distinguish,categorize, cluster, distribute, rank, compare, associateand correlate) that one can perform for data analysis.In Hibino’s study [36] of a data set of tuberculosis,seven high-level tasks include prepare, plan, explore,present, overlay, reorient, and other.

This paper models all tasks as processes that mapthe data space D, the layout space L, and the knowl-edge space K to a result space R. Note that, ourgraph visualization model differs from the van Wijkmodel [78] by the task model. The result space Rmay be a simple boolean space {true, false}; or morecommonly it is a multidimensional space, with eachdimension modelling a separate subtask.

Tasks are often executed by users or data analysers.However, tasks are not necessarily performed by the


same person, who creates the pictures from the data.Furthermore, tasks can be performed directly by ex-tracting the answers from the data with or withoutusing a picture of that data.

The central model for the task process is T =(TD, TL, TK), where TD, TL and TK are three func-tions:

TD : D → R

TL : L → R

TK : K → R.

We extend this common notion with two less com-mon notions TD and TL. These functions are moreabstract; they do not take the users perception orknowledge into account. The function TD returnsa result directly from the data. Intuitively, one canimagine that TD is computed by a “data oracle”, whocan extract a result perfectly from the data.

Similarly, one can think of the function TL as re-turning a result directly from the picture. Again, onecan imagine a “picture oracle”, who extracts perfectresults from the picture. If the visualization mappingcreates a picture that is not entirely consistent with thedata, then it is possible for the picture oracle to returna different result from the data oracle. In this way, thepicture oracle may be limited by the faithfulness of thevisualization mapping.

In this model, all the details (such as questions)of a task are considered less important. It is simi-lar to how we do ignore the details (such as algo-rithms/mechanisms) of a visualization method. Thus,our model is not concerned with specific questions oftasks.

This task model is perhaps over-simplistic; for ex-ample, it does not model the a priori knowledge ofthe human. In addition, the task process can be mademore general by taking some combination of data,layout and knowledge and then mapping to the resultspace. However, the simple model is sufficient todemonstrate the concept of faithfulness - task faith-fulness. We use this simple model of task throughoutthe rest of the paper.

4 FAITHFULNESS MODEL

Informally, a graph visualization is faithful if the un-derlying network data and the visual representationare logically consistent. In this section, we developthis intuition into a semi-formal model. In fact, wedistinguish three kinds of faithfulness: informationfaithfulness, task faithfulness, and change faithfulness.Then we discuss the difference between faithfulnessand correctness, and then between faithfulness andreadability.

4.1 Information faithfulness

The simplest form of faithfulness is information faith-fulness. This is based on the idea that the visual

representation of a data set should contain all theinformation of the data set, irrespective of tasks. Interms of the notation developed above, a visualizationV is information faithful if the function V is injective,that is, V has an inverse.

As an example, consider the classical barycenter

visualization function that takes as input a planargraph G = (N,E), places nodes from a specified faceon the vertices of a convex polygon, and places everyother node at the barycenter of its neighbors (see [72]).This function is information faithful on internally tri-connected (see [72]) planar graphs. However, if theinput graph is not internally triconnected, then samepicture can result from several input graphs (eachinternal triconnected components is collapsed onto aline), and the method is not information faithful.

4.2 Task faithfulness

The intuition behind task faithfulness is that the vi-sualization should be accurate enough to correctlyperform tasks. In terms of the functions V and Tdefined above, a visualization V is task faithful withrespect to specification s ∈ S if

TL(V (d, s)) = TD(d) (3)

for every data item d ∈ D.If a visualization is information faithful, then clearly

it is task faithful, assuming the picture oracle can ex-tract all information from the picture to perform tasks.In many practical cases, such extraction may dependon the perception skills of the viewers. However, theconverse may not hold.

Consider, for example, a visualization function Vcir

that draws all nodes a graph G on the circle. Clearly,Vcir is information faithful; Figure 3a is an example, inwhich we can find all nodes and edges in the drawing.Further, Vcir is task-faithful: all the data is representedin the drawing, and so all tasks can be performedcorrectly using the drawing.

On the other hand, Figure 3b shows a graph draw-ing using edge bundling. Consider the task to estimatethe number of edges between two contiguous groupsof nodes on the boundary of the circle. Another taskis to determine if there is a link connecting groupsof nodes. The edge bundled drawings are certainlytask-faithful for these tasks. However, it is not in-formation faithful, as the original graph is no longerreconstructable from the bundled layout.

4.3 Change faithfulness

The intuition behind change faithfulness is that achange in the visual representation should be consis-tent with the change in the original data. Note thatthis is a different concept to the mental map [18]or stability [63]; while these concepts are concernedwith the user’s interpretation of change, the concept


Fig. 6. Interaction groups between Health researchers

in the EuroSiS dataset

of change faithfulness is concerned with the geometryof change.

Change faithfulness is important in dynamic set-tings, such as interactive or streamed graph drawing.However, it is also valid in static settings, because thedifference between two pictures should be consistentwith the difference between the two data items thatthey represent.

Consider, for example, a function Vgroups that visu-alizes the interaction networks d that occur betweenEuropean Science in Society researchers in Health3.

Suppose that Vgroups uses a force directed algorithmto draw the connected components of a graph d ∈ Dseparately, and arranges these components horizon-tally across the screen, as in Figure 6. Note that Vgroups

is information faithful. However, Vgroups is not changefaithful, because a small change in the graph d (suchas adding an edge) can result in a large change in thepicture.

4.4 Remarks

4.4.1 Faithfulness and readability

More importantly, faithfulness is a different concept toreadability. Readability is well studied in the GraphDrawing literature. It refers to the perceptual andcognitive interpretation of the picture by the viewer.Readability depends on how the graphical elementsare organized and positioned. It does not dependon whether the picture is a faithful representation ofthe data. We can divide the readability concept intothree subconcepts in the same way as we dividedfaithfulness:

1) Information readability: A drawing is information-readable if the perception function P is one-one;that is, if two pictures appear the same to theuser, then they are pictures of the same graph.Effectively, this is saying that all the informationfrom the picture can be perceived by the human.

2) Task readability: A visualization is task-readable fora task T = (TD, TL, TK) if TK(P (ℓ)) = TL(ℓ) forevery layout ℓ ∈ L.

3) Change readability is the classical mental map.

3. Available at http://wiki.gephi.org/index.php/Datasets. Datause in this example are filtered for Health researchers only.

A good graph visualization method should achieveboth faithfulness and readability; in practice, however,there may be a trade-off between the two ideals. Thisis especially true with large graphs, when the data sizeis too large for the visualization to be information-faithful; indeed, the number of pixels may be smallerthan the graph size. In such cases, faithfulness issometimes be sacrificed for readability. In specificdomains, there are important tasks for which thevisualization can be both readable and task-faithful.

4.4.2 Faithfulness and determinism

Faithfulness is a different concept than the idea ofdeterminism. Determinism refers to the requirementthat applying the same visualization on the samegraph should give the same or similar results. Forexample, tree drawing algorithms are deterministic,whereas other graph drawing algorithms, such asspring-embedder, are non-deterministic.

Determinism is an important criterion for visualexploration and navigation of graphs. However, avisualization method may either be deterministic ornon-deterministic, while aiming for faithfulness.

5 FAITHFULNESS METRICS

Faithfulness is not a boolean concept; a visualizationmethod may be a little bit faithful, but less than 100%faithful. Often, one may not tell whether a picture isabsolutely faithful or unfaithful. But one can compareif a picture is more faithful than the other picture ofthe same data.

The classical concept of readability of a graph draw-ing can be evaluated using a number of metrics. Theseinclude, for example, the number of edge crossings,the number of edge bends, and the area of a griddrawing. These readability metrics are formal enoughthat the problem of constructing a readable graphdrawing can be stated as a number of optimizationproblems; thus optimization algorithms can be used.There is not really a clear winner amongst the met-rics, and there is not a single readability metric. Forexample, edge crossing number does not equal to thegraph readability as a graph with one more crossingsis not necessarily “less readable”.

We aim to create a list of faithfulness metrics thatplay the same role. Yet we should emphasize that thefaithfulness metrics proposed in this section are justthe examples to show the “possibility”; they are notthe only ways to define measurement of the faithful-ness concepts. Furthermore, we do not aim to createa generic “faithfulness number”, but we try to showhow quantitative measurements of the faithfulnessconcepts are possible.

In this section we develop a framework for suchmetrics. We assume that the spaces D, L and R eachhas a norm, which we generically denote by ‖ · ‖.

http://wiki.gephi.org/index.php/Datasets


• First, each data item d in data space D can bemodelled in multiple dimensional space A1×A2×· · ·×Ai, where Ai is the i-th attribute dimension.A norm in data space D can be Euclidean norm(‖ · ‖2), or Manhattan norm (‖ · ‖1), or p-norm(‖ · ‖p).

• Second, norms in result space R can be definedin a similar manner of the norm in data space D.

• Third, for layout space L, a definition of normscan be a bit more complex. Layout space L canbe modelled as R

3×C1×· · ·×Ci, where Ci is i-thdimension of visual attributes. In a visualization,visual attributes of nodes include location, color,shape, transparency, texture, etc; while visual at-tributes of edges may further include edge bends.

Further, we assume that each of these spaces hasa distance function ∆ that assigns a positive realnumber ∆(a, b) to each pair a, b of elements of thespace.

5.1 An example of information faithfulness met-rics

The simplest way to measure the information faith-fulness of a graph visualization function V with aspecification s, is to measure its “ambiguity”.

For each data d and visualization ℓ = V (d, s) ∈ L,let V −1(ℓ) denote the set {(d, s) ∈ D×S : V (d, s) = ℓ}.Let |V −1(ℓ)| denote the number of elements in V −1(ℓ).Then the information faithfulness of V is a function finfo,defined by

finfo(d, ℓ) =1

|V −1(ℓ)|. (4)

The metric can have values ranging from 1 (veryfaithful) to 0 (unfaithful).

A more subtle approach is to measure the informa-tion faithfulness of a graph visualization function V asthe information loss in the channel. The loss of infor-mation during the visualization process is defined asentropy in information theory. The information loss iseasier to measure than the total information content ofa data set. There are several techniques for measuringinformation content and information loss (for a fulldiscussion, see [67]).

5.2 An example of task faithfulness metrics

We can measure task faithfulness as the differencebetween the result from the data d and the result fromthe visualization ℓ = V (d, s). The task faithfulness of Vis a function ftask, defined by:

∆task(d, ℓ) = ∆(TL(ℓ), TD(d)) (5)

with respect to the task T = (TD, TL, TK) and specifi-cation s ∈ S. One could define a normalized versionof ftask as:

ftask(d, ℓ) = 1/(∆task(d, ℓ) + 1). (6)

The metric can have values ranging from 1 (very task-faithful) to 0 (task-unfaithful).

Our task faithfulness metric is kept simple enough;we neither take the transformation from data to taskresult, nor the interpretation of the users from thedrawing to task result. In fact, different users mayperceive a drawing differently in many practical cases.

5.3 An example of change faithfulness metrics

Tufte [77] defines the “lie-factor” as the ratio of changein a graphical representation to the change in the data.We can express Tufte’s concept in terms of our model.Then, for a visualization V with specification s ∈ S,the lie factor for two distinct data d, d′ ∈ D with d 6= d′

is defined by:

lie(d′, d, ℓ′, ℓ) = ∆(ℓ, ℓ′)/∆(d′, d),

where ℓ = V (d, s) and ℓ′ = V (d′, s). Tufte’s aim is tomeasure the quality of static visualizations in terms ofthe lie-factor, but we can apply the same principle ina dynamic setting. In the ideal case (no “lie”), the lie

metric has the value of 1.Intuitively, the lie factor increases as change faith-

fulness decreases, and so for two “distinct” data ele-ments d′ and d we can measure the change faithfulness(normalized) as:

fchange(d′, d, ℓ′, ℓ) = exp(−lie(d′, d, ℓ′, ℓ)) (7)

The values of this change metric can vary from 1 (verychange-faithful) to 0 (change-unfaithful).

6 EXAMPLE 1: MULTIDIMENSIONAL SCAL-ING AND FORCE DIRECTED APPROACHES

This section discusses the multidimensional scaling(MDS) [8] and force directed approaches to GraphDrawing [16], [22], [24], [28], [39] in terms of faith-fulness.

The MDS approach to Graph Drawing works asfollows. The input is a graph G=(N ,E), and a |N | ×|N | matrix of dissimilarities δu,v. The goal is to mapeach node u ∈ N to a point pu ∈ R

k such that thegiven dissimilarities δu,v are well-approximated bythe distances du,v=‖pu−pv‖. The set of points pu formsthe layout ℓ = V (G) of G. In practice, k is commonly2 or 3. In most applications, δu,v is chosen to be thegraph theoretic distance between nodes u and v.

To measure the success of an MDS function, a“stress” [49] function is commonly used to computethe distortion between dissimilarities δu,v and fitteddistances du,v. In the simplest case, the stress of alayout ℓ ∈ L is:

stress(node)(ℓ) =∑

u6=v

(δu,v − du,v)2, (8)

MDS can be seen as an optimization problem wherethe goal is to minimize this stress function. Forcedirected algorithms have a similar flavour, but view theproblem as finding equilibrium in a system of forces.



For most MDS approaches, there is a likelihood thatvertices overlap in the “optimal” layout. In thesecases, it is not information faithful, and differentMDS methods would produce the same result fromdifferent data sets.


The stress formula (8) can be seen in terms of ourtask faithfulness framework. Suppose that T is a taskthat depends on the graph theoretic distance betweennodes; let R be the set of real-valued matrices indexedon the node set. For a graph G=(N ,E) ∈ D, let TD(G)be the matrix [δu,v]u,v∈N . Suppose that the visualiza-tion V places node u at location pu; let TL(V (G)) bethe matrix [du,v]u,v∈N . Then define

f(node)task (G) = max

G∈Dn

‖TL(V (G))− TD(G)‖2, (9)

where Dn is the set of graphs of size n and ‖·‖2 is theFrobenius norm. Clearly, minimising task faithfulnessis equivalent to minimising the stress defined by (8).

6.3 Change faithfulness

Further, we can evaluate the change faithfulness of anMDS method. In fact, MDS methods have been usedextensively in dynamic settings, using stress to pre-serve the mental map. Suppose that at time t, we havea graph G(t), and the visualization function places

node u at point p(t)u at time t. A stress function can

calculate the difference between the layout ℓ(t) ∈ L attime t and the layout ℓ(t

′) ∈ L at an earlier time t′:

stress(node)(ℓ(t), ℓ(t′)) =

∑

u∈N

‖p(t)u − p(t′)

u ‖2.

In the so-called “anchoring” approach, t′ is zero; inthe “linking” approach, t′ is the previous time framebefore t (see [6]). These measures, however, aim forthe mental map preservation - or change readability- rather than change faithfulness. For example, theyaim to ensure that if the change in the graph is small,then the change in the layout is small. They do notensure that if the change in the graph is large, thenthe change in the layout is large.

However, we can use the stress approach to definethe lie factor, such as:

lie(d(t′), d(t), ℓ(t

′), ℓ(t)) =

∑u6=v ‖(d

(t)u,v − d

(t′)u,v )/d

(t′)u,v‖

∑u6=v ‖(δ

(t)u,v − δ

(t′)u,v )/δ

(t′)u,v ‖

where d(t)u,v = ‖p

(t)u − p

(t)v ‖ and δ

(t)u,v denotes the graph

theoretic distance between u and v in G(t).Then the normalized change faithfulness can be

measured in terms of the distortion of the data changerelative to the layout change:

fchange(d(t′), d(t), ℓ(t), ℓ(t

′)) = exp(−lie(d(t′), d(t), ℓ(t

′), ℓ(t)))

6.4 Remarks

The force directed and MDS approaches has hadconsiderable impact on the commercial world, despitethe fact that they do not have explicit or validatedreadability goals. We believe that the success of theseapproaches is due to the fact that they have explicitand validated task faithfulness goals with respect totasks that depend on graph theoretic distances. Wesuggest that better MDS methods could be designedby optimising their change faithfulness using the liefactor stress above.

7 EXAMPLE 2: EDGE BUNDLING

Edge bundling, as illustrated in Figure 3b and 4b,has been extensively investigated to reduce visualclutter in graph visualizations. Many edge bundlingtechniques have been proposed, including hierarchi-cal edge bundling [37], geometry-based edge cluster-ing [37], [52], [81], force-directed edge bundling [38] andmulti-level agglometive edge bundling [27], just to namea few.

The US airline networks are typical examples usedfor demonstration of edge bundling methods. Figure 7shows several edge bundling results.

Edge bundling seems to increase task readabilitywith respect to some tasks; for example, the classicbundling of air traffic routes in the USA (see [38],[74]) seems to make it easier for a human to identifythe main hubs and flight corridors. However, somereadability metrics are sacrificed; for example, thenumber of bends is increased, making individualpaths difficult to follow (the authors are not awareof any human experiments that measure readabilityfor edge bundling). In this Section we make someremarks about the faithfulness of edge bundling.


Edge bundling reduces information faithfulness: asmore edges are bundled together, it becomes harder toreconstruct the network data from a bundled layout.We can propose a rough-and-ready metric for thisreduction based on the model presented in Section 5.Given an input graph G = (N,E), an edge bundlingvisualization process V partitions E into bundles E =B1∪B2∪. . .∪Bk. Let Gi denote the subgraph of G withedge set Bi and node set Ni consisting of endpoints ofedges in Bi. Edge bundling methods ensure that Gi isbipartite; suppose that Ni = Xi ∪ Yi is the bipartitionof Gi. In the bundled layout, Gi is indistinguishablefrom a complete bipartite graph on the parts Xi andYi. This representation has inherent information loss.Let xi = |Xi|, and yi = |Yi|. The number of (labelled)bipartite graphs with parts Xi and Yi is 2xiyi . Thus if

q =∑k

i=1 xiyi, then there are 2q graphs that have thesame layout as G. This can be used as a simple modelfor computing the information faithfulness of V .


(a) FDEB [38] (b) IBEB [74]

Fig. 7. Examples of US airline network visualizations using edge bundling

(a) cycle vs. stress ratio (b) number of control points vs. stressratio

Fig. 8. Comparisons of the faithfulness of the edge bundled worldcup visualizations


Most bundling methods use a compatibility function;roughly speaking, a compatibility function C assignsa real number C(e, e′) to each pair e, e′ of edges. Twoedges e and e′ are more likely to be bundled togetherif the value of C(e, e′) is large. A number of compati-bility functions have been proposed and tested; theseinclude spatial compatibility [38] from length, position,angle and visibility between edges, semantic compati-bility, connectivity compatibility, importance compatibil-ity and topology compatibility. Some of these functionsdepend only on the input graph G, and some dependalso on the layout of G.

For a number of tasks, such as identifying hubs in anetwork, highly compatible edges are equivalent; thecorrect performance of such tasks does not dependof distinguishing between them. Here we show thatstress functions can be used to define metrics forcomputing the task faithfulness of the edge bundledlayout relative to such tasks.

Given a pair of edges e and e′ in an input graph G,let C(e, e′) denote their compatibility. We assume thatthis compatibility function depends only on G andnot on its layout. Let ℓ ∈ L be the layout of G. Fortwo edges e and e′, let d(e, e′) be the distance betweenthe curves representing e and e′ in ℓ. We can choosefrom a number of distance functions for curves, suchas the Frechet distance and several distance measuresfor point sets. The stress in ℓ is then defined as:

stress(edge)(ℓ) =∑

e6=e′

(C(e, e′)− d(e, e′))2. (10)

7.3 Remarks

Despite the plethora of recent papers in edgebundling [44], there are few evaluations of effective-ness. Using the formal models outlined above, one canbegin to evaluate faithfulness and compare bundlingmethods. For example, one can test the followinghypotheses:

Hypothesis 1: The force-directed edge bundling(FDEB) [38] methods and its force-directed vari-ants [47], [60], [70] are task-faithful.

Hypothesis 2: Force-directed edge bundling meth-ods are more task-faithful when using more controlpoints per edge.

We have conducted several experiments with thefaithfulness metrics. We use the worldcup data4 asour examples. Our initial studies using the metricsabove have shown a confirmation of the above hy-potheses. Figure 8 shows statistics of stress valuesat different iteration cycles of force-directed edgebundling algorithm (FDEB) [38]. The figure has shownthat FDEB achieves more faithful results when morenumber of iterations are performed. Furthermore, inlater iterations, the result becomes more faithful asthe algorithm uses more control points to improve itslayout.

8 EXAMPLE 3: VISUALIZATION METAPHORS

This section discusses our new notions of faithful-ness for several representative graph visualizationmetaphors.

4. Data available at http://gd2006.org/contest/WCData/

http://gd2006.org/contest/WCData/


Fig. 9. Trade map between countries [25]

8.1 Matrix representation

Besides node-link diagrams, visualization of graphsas matrices form is also popular. In fact, matrix andnode-link diagrams have different characteristics andcan be used as suitable representations for differenttasks and datasets.

Generally speaking, matrix metaphor is very faith-ful. All the nodes and edges are represented in thevisualization. Matrices do not suffer from node over-lapping and edge crossing.

However, matrix metaphor is not very task-readable for several tasks. Ghoniem et al. [29] reporttheir studies on the performance of matrix and node-linked diagrams for several low level tasks. Theirresults show that node-link diagrams are in favour ofvery small (20 vertices or less) and sparse networks.Ghoniem et al. also show that matrices are moreeffective even for large graphs, except when the tasksare related to path tracing. Path-related tasks (such aspath tracing between nodes or finding a shorted pathfor a pair of nodes) are the weakness of matrices; thisknown problem is reported in the study of Ghoniemet al. [29].

For certain tasks, matrix representations are moretask-readable than node-link diagrams. For example,for tasks such as locating and selecting nodes, thisrepresentation is more appropriate as node labels areoften more readable. Matrices do not suffer from edgecrossing, which is the most trouble-some for viewingnode-link visualization of dense graphs. Lastly, matri-ces could give an immediate overview of the sparseand dense regions within a network as well as thedirectedness of the connections.

A number of methods aim to improve readabil-ity of the matrix metaphor. For example, reorderingcolumns/rows to show highly connected groups ofnodes [33], [64] increases readability without sacrificefaithfulness.

The matrix metaphor often requires a quadraticspace (of the number of nodes) to display. To visualizelarge graphs, information-reduction methods such ascollapsing rows and columns are applied. However,such information-reduction methods increase read-ability and sacrifice faithfulness.

Fig. 10. A Hybrid Visualization of Social Networks [35]

8.2 Cartography

Map-based approach is a promising way to produceappealing visualizations of graphs [25], [30], [40].In map-based visualization, a set of “countries” aredrawn on the plane (see Figure 9). Each country en-capsulates a node or a set of nodes within its bound-ary. Edges are then drawn to connect its adjacentnodes. The visualization produced by this approachappears appealing and looks like a typical geographicmap that ones usually see. Maps have been studiedto display changes and trends in dynamic data [55]and stream data [26].

These map-based approaches increase task faith-fulness for many tasks, such as identifying clustersor similar topics. However, map-based approachessometimes sacrifice information faithfulness. For ex-ample, links with small weights are sometimes dis-carded to enable users to focus on more importantlinks and to create appealing maps with more read-able boundaries.

8.3 Compound visualizations

Compound visualization techniques combine severaltypes of visualization metaphors into the final re-sult. Examples of compound visualizations includeMatLink [34] and NodeTrix [35], which integrate ma-trix views with node-link diagrams.

Figure 10 shows an example of the hybrid visu-alizations by NodeTrix [35]. NodeTrix proposed byHenry et al. [35] integrates node-link diagrams toshow the global structure of the network and matrix-representation of groups of nodes. Thus, the methodreduces the complexity and clutter of the network,while still providing all the information.

In general, these techniques [34], [35] seem to in-crease readability for some parts of the networksthat are of most interest and at the same time maysacrifice faithfulness and readability in other partsof the network that are less important. Furthermore,there can be a trade-off between global readability andlocal readability, and between global faithfulness andlocal faithfulness.

9 DISCUSSIONS AND FUTURE WORK

This section discusses some important factors in vi-sualization that have direct impacts on visualization


research, and their implications on the faithfulnessconcepts.

Research in visualization in general and graph vi-sualization in particular is influenced by two mainfactors: (1) display capacity (hardware), and (2) inter-action. The former is related to the availability of dis-play resources. The latter refers to the development ofnovel interaction methods to adapt the main displayparameters such as the level of details, data selectionand aggregation. These factors have a major impact onhow the data is presented. We discuss each of thesebelow.

9.1 Faithfulness and correctness

We should stress that faithfulness is a different con-cept to the classical idea of correctness of an algorithm.An algorithm is correct if it does what it is requiredto do; correctness is an essential property of everyalgorithm. However, a visualization method may doexactly what it is required to do without achievingfaithfulness.

9.2 Faithfulness in space and time

The concepts of faithfulness (information-, task- andchange-faithfulness) are mostly concerned with the“space” dimension. That is, the visual mapping fromdata d ∈ D to image l = V (d) ∈ L does not (explicitly)consider the “time” dimension.

We can extend the faithfulness concepts to integratethe time dimension. Let T denote the time domainand let t ∈ T be a time point. A graph d at time t canbe presented by a two-dimensional data item (d, t) ofthe graph d and the time t. The visualization processV transforms the two-dimensional data item into:

• a drawing V (d, t) in which the drawing of V (d)is placed at a location in space determined by t(in small-multiple display approach).

• a drawing V (d) at a time frame V (t) (in animationapproach).

Dynamic graph visualizations often considers thesequential number of the graph d in the sequence ofinput graphs as the time t; in other words, V (t) = t isan identity function. Thus, the faithfulness conceptsmay disregard the time factors in these cases withoutloss of accuracy. However, when time t is consideredin a more general setting, we should consider thefollowings:

Small-multiple approaches: (1) The Informationfaithfulness should consider the reversibility of thetime t; for example, placing graph elements of d ata time t close together and avoid mixing elements ofdifferent times. (2) Task faithfulness should considerthe accuracy of task performance regarding the timeattributes. For example, one should correctly identifyif two data elements belong to the same time or not.(3) Change faithfulness should further consider the

change in time in the final visualizations. For example,two graphs d at time t and d′ at time t′ are placed closetogether if |t − t′| is small; or placed far if |t − t′| islarge.

Animation approaches: The transformation of timet to V (t) can be, for example, the identity function, alinear function, a sequence-based function, or a non-linear function. (1) Information faithfulness shouldconsider the inversibility of the time t; for examples,place graph elements of d at a time t in a sepa-rate frame t. (2) Task faithfulness should considerthe accuracy of task performance regarding the timeattributes. For example, one should correct identifywhether or not a graph element exists at time t.(3) Change faithfulness should further consider thechange of graphs together with the change in time inthe animation. For example, two graphs d at time tand d′ at time t′ appear at frames V (t) and V (t′) thatare close/far in the animation if |t− t′| is small/large.

9.3 Display device

Although there have been numerous revolutions inhardware technologies, screen size is still a preciousbut limited resource. Technically speaking, “screensize” refers to the number of pixels in a display ratherthan the physical dimensions of the screen. Examplesof displays include the high-resolution displays, large-scale power walls and small portable devices.

Faithfulness metrics should be addressed in a spe-cific formula depending on the characteristics of theavailable output devices. For visualizing large datasets, the large number of data elements can com-promise performance or overwhelm the capacity ofthe viewing platform. In addition, visualization meth-ods should take user-centric requirements (from userinputs or interactions) into account to produce bestresults that balance between faithfulness and readabil-ity.

9.4 Interaction

Ideally, the user interface and interaction techniquesshould be simple enough to help users to performthe tasks with less cognitive efforts; a complex userinterface may sometimes distract the users. Novelinteraction techniques need to seamlessly supportvisual communication (user inputs) of the user withthe system. For example, when a user may need toexplore and edit a certain part of the graph severaltimes, the system can capture the users’ area of inter-est. The layout adjustment algorithms should adaptto user needs and should cleverly sacrifice the overallfaithfulness to the local faithfulness (of the part of thegraph of user interests).

The below are the implications of our faithfulnessconcept from three specific types of interactions.

Affine transformation: Intuitively, faithfulness doesnot depend on global affine transformations such


TABLE 1Faithfulness and readability

Faithfulness Readability

Information• The data set is faithfully represented by

the picture.• All the original data is in the picture.• The visualization process is injective.

• The user perceives the all the data in thepicture.

• The perception process is injective.

Task• The picture contains enough data to cor-

rectly perform the task• The user perceives enough data from the

picture to correctly perform the task.

Change • Changes in the picture are consistent withchanges in the data.

• The mental map is preserved.• The user can remember one screen from

the previous screen.

TABLE 2

Faithfulness of existing visualization methods

Faithfulness Readability

Visualization Info

Task

Ch

an

ge

Info

Task

Ch

an

ge

Force-directed - + + - + -MDS - + + - + -Edge concentration - + - - + -Confluent drawing - + - - + -Edge bundling - + - - + -Matrix metaphor + + + + - -Map-based metaphor - + + + + -Combination - + + - + +

as rotation, translation and scaling. As long as thedrawing is consistent with the data, the visualizationis considered faithful. On the other hand, a (partial)transformation of the local parts of the graphs mayincrease readability of these parts of the graphs, yetmay degrade faithfulness of other parts of the graphs.

Distortion techniques: such as lens effects and occlu-sion reduction can provide the analyst with trade-offbetween faithfulness and visual clarity. These meth-ods typically transform object’s position to improvelocal readability at the cost of accuracy of globalrelations.

Level of detail: Relevant data patterns and relation-ships can be visualized in several levels of detail atappropriate levels of data and visual abstraction. Theoverall goal is to balance between faithfulness andreadability to maximize user expectations.

10 CONCLUDING REMARKS

This paper has introduced the concept of faithfulnessfor graph visualization. We believe that the classicalreadability criteria are necessary but not sufficientfor quality graph drawing; faithfulness is a genericcriterion that is missing.

The paper has described the faithfulness conceptin a semi-formal model. We have distinguished threekinds of faithfulness: information faithfulness, task

faithfulness, and change faithfulness. Table 1 gives asummary of these faithfulness concepts.

Based on the visualization model and the faithful-ness concepts, we have also presented a model forfaithfulness metrics. In Section 6, 7 and 8, we illustratethe faithfulness concept with three examples.

• The first example is multidimensional scaling /force-directed methods. We believe that futuredirections of these methods would need to bal-ance the aims of readable outputs versus faithfulrepresentations.

• The second example is edge bundling. Despite arecent upsurge of interest in edge bundling, thereare very few evaluations; we show that faithful-ness metrics may prove the key to evaluation.

• The last example includes matrix metaphorsand map-based visualizations. These methods areuseful for large graphs; we show that future di-rections of these methods would need to balancebetween global / local readability versus global/ local faithfulness.

10.1 Guidelines

Table 2 summarizes the faithfulness of some selectedvisualization methods. In this table, ‘−’ represents ‘no’or ‘low’; ‘+’ represents ‘yes’ or ‘high’. These resultsmay give readers a reference, which may not be thesame with the readers’ viewpoints.

A ‘+’ for task faithfulness should be interpreted as:a method is faithful for some tasks, rather than faithfulfor all tasks. In Section 6, 7 and 8, we describe severalspecific tasks, in which these visualizations are task-faithful.

10.2 Remarks on 3D drawings

We conclude this paper with a remark about 3D graphdrawing. The occlusion problem for 3D means that,even with binocular displays, some part of the graphis always hidden. This can be seen as a lack of notonly readability but also information faithfulness. We


suggest that the lack of commercial impact of 3Dgraph drawing is partially due to its inherent lack offaithfulness.

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Quan Hoang Nguyen Quan Nguyen is a post-doc research fellowat the School of Information Technologies, University of Sydney,Australia.

Peter Eades Peter Eades is an Emeritus Professor at the School ofInformation Technologies, University of Sydney, Australia.

http://www.cs.brown.edu/~rt/gdhandbook/

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