Graph drawing aesthetics and the comprehension of UML class diagrams: an empirical study pptx

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Graph drawing aesthetics and the comprehension of UML classdiagrams: an empirical studyHelen C. Purchase, Matthew McGill, Linda Colpoys and David CarringtonSchool of Information Technology and Electrical EngineeringUniversity of QueenslandSt Lucia, Brisbane 4072, Queensland{hcp, davec}@itee.uq.edu.auAbstractMany existing automatic graph layout algorithms are unrelatedto any particular semantic domain. Designers of such algorithmstend to conform to layout aesthetics, and claim that by doing so,the resultant diagram is easy to understand. Few algorithms aredesigned for a specific domain, and there is no guarantee that theaesthetics used for generic layout algorithms will be useful forthe visualisation of domain-specific diagrams (for example,visual programs, or entity-relationship diagrams). This paperdescribes a study which aimed to identify the most importantaesthetics for the automatic layout of UML class diagrams froma human comprehension point of view. The results suggest thatfor specific domains, the actual semantics of the given graphmay need to be considered before an appropriate graph drawingcan be produced. !Keywords: UML class diagrams, graph layout aesthetics, humanperformance.IntroductionCASE tools which provide support for UMLdiagramming (eg Rational Rose (Rational Rose 2001),Microsoft Visio (Microsoft Visio 2001), EnterpriseArchitect (Enterprise Architect 2001)) can benefit fromthe use of an automatic layout tool. Thus, once the userhas created a UML diagram, or added new objects andrelationships to an existing diagram, a graph layout toolcould automatically re-position the objects and lines sothat the diagram is more comprehensible.Many automatic layout algorithms already exist (Battistaet al. 1994): they take as input a relational graph structureof objects and the relationships between them, andproduce a visual representation of the information indiagrammatic form. The designers of these algorithmstend to optimise certain aesthetic criteria (Coleman andStott Parker 1996), and claim that by doing so, theresultant graph drawing helps the reader to understand theinformation embodied in the graph. (These "aestheticcriteria" have been defined and subsequently used ingraph layout algorithms by researchers of automaticgraph layout algorithms: they do not necessarily relate tothe notion of "aesthetically pleasing" with respect to pre-attentive visual perception.) However, these algorithms Copyright ' 2001, Australian Computer Society, Inc. Thispaper appeared at the Australian Symposium on InformationVisualisation, Sydney, December 2001. Conferences inResearch and Practice in Information Technology, Vol. 9. PeterEades and Tim Pattison, Eds. Reproduction for academic, not-for profit purposes permitted provided this text is included.have typically been defined with respect to abstract graphstructure (i.e. nodes and relationships that have norelationship to objects in the real world), and also havenot taken any account of human computer interactionissues relating to diagram comprehension.If CASE tools are to benefit from the use of theseautomatic layout algorithms, it is important that the mostappropriate algorithm, embodying the most appropriategraph layout aesthetic criteria, be chosen to ensure thatthe diagrams produced are suitable for humancomprehension in the intended CASE domain.Recently, some human experimental work has beenperformed on the aesthetics underlying common graphdrawing algorithms (Purchase 1997): these have shownthat the aesthetics of minimising crosses and bends, andmaximising symmetry may assist with humanperformance in graph theoretic tasks on abstract graphdrawings. These initial experiments were domain-independent: the graphs used embodied meaninglessobjects and relationships. There is no guarantee that theresults of these domain-independent experiments wouldnecessarily transfer across to the domain of UMLdiagrams.Some preliminary work has been done on subjects’preference for different aesthetics in UML class andcollaboration diagrams (Purchase et al. 2000), revealingthat users preferred diagrams with fewer bends andcrosses, shorter edge lengths and an orthogonal structure.However, that experiment only looked at subjects’personal preference for the aesthetics, rather than theirperformance on UML related tasks.This paper describes two experiments that aimed todetermine which graph drawing aesthetics are mostimportant for the display of UML class diagrams, notwith respect to computational efficiency, designers’preference, or even subjects’ preference, but with respectto the extent to which the aesthetics produce diagramsthat are easy for subjects to understand. The twoexperiments had identical methodology: the differencebetween them was in the manner in which theexperimental diagrams were produced. In experiment A,aesthetics were measured computationally; in experimentB, they were measured perceptually.1.1 Experimental aimThe aim of this study was to determine which of theaesthetics underlying common graph drawing algorithmsare most suited to human comprehension of UMLdiagrams. By asking subjects to perform comprehensiontasks on the same UML diagram portrayed with differentaesthetic emphases, we aimed to identify the aestheticcriteria that resulted in the best performance. Twoexperiments were conducted: the first (Experiment A)used computational metrics to determine the presence ofdifferent aesthetics in the UML diagrams used; thesecond (Experiment B) included a preliminary perceptionexperiment which asked for subjects’ opinions on theextent of the aesthetics in the diagrams.1.2 UML class diagramsUML class diagrams are used to describe the static viewof an application (Rumbaugh et al. 1999): the mainconstituents are classes and their relationships. A class isa description of a concept, and may have attributes andoperations associated with it. Classes are represented asrectangles. A relationship between two classes is drawnas a line. Inheritance relationships indicate that attributesand operations of one class (the "superclass") areinherited by other classes (the "subclasses"), withoutneeding to be explicitly represented in the subclassesthemselves.Figure 1 is an example of a small UML class diagram,showing the relationships between the classes in a vehiclehire organisation, including inheritance relationshipsbetween the vehicle, car and truck classes.-name : StringCompany-name : StringEmployee-registration number : StringVehicle-mass : intTruck-transmission : StringCar1 *1*1*hiresemploysdrivesFigure 1: Example UML class diagram.1.3 Aesthetic criteriaFive graph drawing aesthetics were used in experiment A:• (b) Minimise bends (the total number of bends inpolyline edges should be minimised (Tamassia 1987))• (n) Node distribution (nodes should be distributedevenly within a bounding box (Coleman and StottParker 1996))• (ev) Edge variation (edge lengths should be uniform(Coleman and Stott Parker 1996))• (f) Direction of flow (a consistent direction of edgeflow (Waddle 2000))• (o) Orthogonality (fix nodes and edges to anorthogonal grid (Tamassia 1987, Papakostas andTollis 2000))A further two aesthetics were included in experiment B:• (el) Edge lengths (edge lengths should be short; edgelengths should not be too short (Coleman and StottParker 1996))• (s) Symmetry (where possible, a symmetrical view ofthe graph should be displayed (Eades 1984, Gansnerand North 1998))Experiment A1.4 Experimental materials:1.4.1 The application domainThe class diagram used was based on a simple domain,which models a small Information Technology companythat employs consultants, programmers andadministrative staff to undertake projects for clients. Theexample includes 13 objects, 12 associations and 5inheritance relations (see Figure 2).A textual specification of this domain was produced insimple English. The subjects were asked to match theexperimental diagrams against this specification.1.4.2 UML tutorial and worked exampleA tutorial sheet explained the meaning of UML classdiagrams, and, using a simple example, described itssemantics. Subjects were not expected to have any priorknowledge of UML, and this tutorial provided all theUML background information they required for theexperimental task. A worked example demonstrated thetask that the subjects were to perform, by presenting asmall specification with four different diagrams, and foreach diagram indicating whether it matched the givenspecification or not. Care was taken to ensure that neitherthe tutorial nor the worked example would bias thesubjects towards one layout over another.1.5 The experimental diagramsThe experimental diagrams were produced according tocomputational metrics that measured the presence of eachaesthetic in a diagram (Purchase 2001). These metricswere scaled to lie between 0 and 1, where 1 means apositive amount (i.e. an amount of the aesthetic for whichit is assumed the drawing is easier to read: few bends,high degree of orthogonality, low edge variation, evennode distribution, upward flow).-number : Integer-balance : CurrencyBank Account-title : StringAdministrator1-name : String-staffID : IntegerStaff-specialty : StringConsultant-title : StringReport1-name : StringClient1*-title : StringProject1***-name : StringHardware-name : StringSoftware1Junior ProgrammerSenior Programmer1 *-languages : StringProgrammer**-meetings : StringSchedule* 11*planssupervisesorganisesmanagessubcontractsapprovesproducesruns onworks onused indevelopsconsults1111***Figure 2: The UML class diagram used for both experiment A and experiment B.For each aesthetic, a "low-effect" (-) and a "high-effect"(+) version of the diagram was produced.1 To ensure thatthere were no confounding factors between the aesthetics,the ranges were controlled as much as possible. Forexample, to remove any confounding factors in a diagrampair for a particular aesthetic, the measurement of allother aesthetics were kept within a "middle-effect" range.This ensured that any significant difference in theperformance of a low-effect diagram with respect to itshigh-effect counterpart could be attributed to the relevantaesthetic, rather than to any other aesthetic variationwithin the diagram pair.Prior work has shown conclusively that edge crossingsare an impediment to human comprehension of graphdrawings (Purchase et al. 1995, Purchase 1997), so alldiagrams had no edge crossings.A control diagram that conformed to a "middle-effect"range for all the aesthetics as much as possible was alsocreated. There were therefore a total of 11 experimentaldiagrams.In addition, a second middle-effect diagram wasproduced: this was the example diagram that was given tothe subjects during the preparation period.Table 1 shows the aesthetic values for all the diagrams. 1 Note that, because of the way the metrics have beendefined, "low-effect" diagrams embody an amount of theaesthetic for which it is assumed the diagram would bedifficult to read (for example, many bends, a widevariation in edge lengths), while "high-effect" diagramsembody an amount of the aesthetic for which it isassumed the diagram would be easy to read (for example,a majority of the directed edges pointing upwards, aneven distribution of node positioning)Ten incorrect diagrams were created by randomlychanging the origin or destination of one relationship perdiagram. The layouts of the incorrect diagrams werevisually comparable to those of the correct diagrams: aswe did not intend to analyse the responses to the incorrectdiagrams, their layout was not important. However, itwas, of course, important to include incorrect diagrams inthe experimental set (so that the correct answer to eachdiagram presented was not the same), and for theseincorrect diagrams to be visually comparable to thecorrect diagrams (so they could not be identified by merevisual pattern matching).1.6 Experimental procedure1.6.1 PreparationThe students were given preparatory materials to read asan introduction to the experiment. These documentsconsisted of a consent form, an instruction sheet, atutorial on UML class diagrams and notation, and aworked example of the experimental task. The workedexample demonstrated the type of error that had beenincluded in the incorrect diagrams.As part of this document set, the subjects were also giventhe textual specification of the UML case study to be usedin the experiment: this was the specification againstwhich they would need to match the experimentalDiagram Aestheticbends (b)orthogonality(o)edgevariation (ev)nodedistribution(n)direction offlow (f)b+ 1 0.43 0.66 0.59 0.6b- 0.71 0.46 0.64 0.56 0.6o+ 0.85 0.70 0.66 0.56 0.4o- 0.85 0.32 0.64 0.56 0.6ev+ 0.85 0.44 0.74 0.59 0.6ev- 0.85 0.41 0.55 0.59 0.6n+ 0.85 0.41 0.66 0.73 0.4n- 0.85 0.48 0.64 0.45 0.6f+ 0.85 0.44 0.65 0.59 1f- 0.85 0.46 0.66 0.59 0control 0.85 0.45 0.66 0.57 0.6example 0.85 0.44 0.66 0.56 0.6Table 1: The computational aesthetic values for the experiment A diagrams.diagrams. The subjects were asked to study thisspecification closely, and memorise it if possible. Theywere also given an example diagram modelling thespecification, with comparable aesthetic metric values tothe middle-effect control diagram.The subjects were given 15 minutes to sign the consentform, read through and understand the materials, askquestions, take notes, or draw diagrams as necessary.1.6.2 Online taskThe subjects then used an online system to perform theexperimental task. A copy of the text specification withthe example diagram was placed in front of the computerfor easy reference, and the UML experimental diagramswere presented in random order for each subject. Thesubjects gave a yes/no response to each presenteddiagram, indicating whether they thought the diagrammatched the specification or not: two keys on thekeyboard were used for this input.16 practice diagrams (randomly selected from the 21experimental diagrams) were presented first. The datafrom these diagrams was not collected, and the subjectswere not aware that these diagrams were not part of theexperiment. These diagrams gave the subjects anopportunity to practise the task before experimental datawas collected.The 11 correct diagrams were presented twice and the 10incorrect diagrams once, a total of 32. The diagrams werepresented in a different random order for each subject, inblocks of eight, with a rest break between each block (thelength of which was controlled by the subject).Each diagram was displayed until the subject answered Yor N, or 50 seconds had passed. A beep indicated to thesubject when the next diagram was displayed after atimeout (which was recorded as an error). The practicediagrams helped the subjects get used to the length of theallocated time period. The timeout period and the timeneeded for the subjects to prepare for the experimentwere determined as appropriate through extensive pilottests.A within-subjects analysis was used to reduce anyvariability that may have been attributed to differencesbetween subjects: thus, each subject’s performance on onelayout was compared with his or her own performance onan alternative layout. The practice diagrams and therandomisation of the order of presentation of theexperimental diagrams for each subject helped counterthe learning effect (whereby subjects’ performance on thetask may improve over time, as they become morecompetent in the task).The response time and accuracy of the subjects’ responsesto the 32 experimental diagrams were recorded by theonline system.1.6.3 SubjectsThe 30 subjects were second and third year ComputerScience and Information Systems students at theUniversity of Queensland. They were paid $15 for theirtime, and, as an incentive for them to take the experimentseriously, the best performer was given a CD voucher.1.7 Results: experiment ABoth the speed and accuracy of each subject’s responseswere measured, enabling the analysis of two differentmeasures of understanding.Average Times051015202530Bends NodeDistributionEdgeVariationFlow OrthogonalityAesthetic VariationsTime (sec)-0+Aesthetic Accuracy020406080100Bends NodeDistributionEdgeVariationFlow OrthogonalityAesthetic VariationsAccuraccy (%)-0+Figure 3: The response time and accuracy results forexperiment A.There were no significant results in the accuracy data:this indicates that the time allocated to the subjects wassufficient for them to correctly classify the diagrams.Thus, only one measurement of understanding wasconsidered - that of the time taken for subjects to respond.Using a two-tailed t-test, the statistically significantresponse time results are: Bendso control is better than b+ (p<0.05) Edge variationo control is better than ev+ (p<0.05)o control is better than ev- (p<0.05) Flowo control is better than f+ (p=0.058, approachessignificance)o f- is better than f+ (p<0.05)1.8 Analysis1.8.1 BendsThe data show that the diagram with a low number ofbends (b+) produced worse performance than the controldiagram (which had a medium number of bends). This isa surprising result, as a previous study showed that in adomain-independent context, performance is improvedwith fewer bends (Purchase 1997), and a UML preferenceexperiment showed that subjects did not like bends(Purchase et al. 2000).A possible explanation for this result may be thatincreased orthogonality requires an increase in thenumber of bends, and therefore the diagram with amedium number of bends may have produced a goodperformance because of an increase in orthogonality.However, the orthogonality values for these two diagramsare not substantially different: 0.43 for b+, and 0.45 forthe control. In addition, the lack of any significant resultsfor the orthogonality diagrams o+ and o- implies thatincreased orthogonality cannot be used as an explanationfor this surprising result.1.8.2 Edge variationThe control diagram (with a medium variation of edgelengths) produced better performance than both ev+ (alledges of similar length) and ev- (some edges very short,some edges very long). This was another surprisingresult, as we had expected that ev+ would produce betterperformance than both the control and ev It appears that widely varying edge lengths is less usefulthan a medium variation of edge lengths: this is asexpected. The improved performance of the control overthe diagram with edges of similar size is difficult toexplain, and led us to believe that perhaps it is the actuallength of the edges (rather than their variation) that maybe important.1.8.3 FlowBoth the results for the flow diagrams show that therewas decreased performance on the diagram with themajority of the edges directed upwards (f+). Again, thisresult is contrary to expectations. A study of UML classdiagram syntax (Purchase et al. 2001) showed animproved performance, and an increased preference, forupward arrows, as it is more intuitive to have thesuperclass placed above the subclasses. As the f+ and f-diagrams were almost mirror images of each other (abouta horizontal axis), there were no obvious confoundingfactors that produced this unexpected result.1.9 DiscussionNone of our expectations were satisfied in experiment A:two of the aesthetics (node distribution and orthogonality)produced no significant results at all, and the significantdata from the other three aesthetics was difficult tointerpret reasonably and consistently.In reassessing the diagrams that we used for thisexperiment, we felt that perhaps the problem was in themeasurement of the presence of the aesthetics. Themetrics, while useful for measuring the aesthetics from acomputational point of view, may be less useful formeasuring perceptual aesthetic presence from a humanpoint of view. For example, the orthogonality metricmeasures the extent to which the nodes and edges areplaced along an underlying unit grid, but the humanperception of orthogonality in a diagram may not matchthe numerical value produced by the metric. Thisphenomenon may particularly be the case for aestheticswhich are global; that is, require an overall assessment ofthe entire diagram, for example, orthogonality, symmetry,or node distribution.We therefore decided to run the experiment again, butthis time with a different set of diagrams. The diagramsfor experiment B would be created according to humans’perception of the presence of each aesthetic in thediagrams, rather than according to the defined metrics.Experiment B1.10 Experimental materials:The application domain, the UML tutorial and workedexample, the preparation period, the online task and thedata collection method were all the same as forexperiment A. The only change to the experimentalprocedure was that the timeout was 40 seconds (ratherthan 50 seconds): this change was due to the fact that asthe diagrams for experiment B were produced accordingto human perception, rather than according tocomputational metrics, they appeared to the subjects to beeasier to read. This timeout period was determined asappropriate through extensive pilot tests. The subject poolfor experiment B was the same as experiment A: therewere a total of 35 subjects for experiment B.1.11 The experimental diagramsThe main difference between experiment A andexperiment B was the way in which the experimentaldiagrams were produced. While experiment A usedcomputational metrics to determine the presence of anaesthetic in a diagram, in experiment B, a separate humanperception study was used to assess the extent to whichaesthetics were perceived in a diagram.Experiment B differed from Experiment A in two otherimportant aspects: choice of aesthetics and aestheticvariation.1.12 Choice of aestheticsExperiment B examined those aesthetics that were testedin experiment A as well as two new aesthetics that it wasfelt may also have an influence on performance. Thesetwo aesthetics were:Edge lengths. For experiment A, we only considered thevariation of the edge lengths. Having got results thatseemed to indicate that a medium-effect edge variation(i.e. a variation in the lengths of the edges which isneither small nor large) produces better performance, wedecided to include edge lengths in experiment B(Coleman and Stott Parker 1996).Symmetry. With respect to graph layout, symmetry isbest considered perceptually rather than computationally.A computational definition of symmetry which merelyconsiders the geometric correspondence of nodes aroundvertical and horizontal axes does not take into accountlocal symmetries, and the tolerance that humans have forperceiving symmetry (i.e. the fact that humans will statethat a square is symmetric even if the pixel values of thecorners are slightly removed from the underlying grid). Acomputational algorithm that takes all local symmetriesand perceptual tolerance into account would becomputationally complex, and can only be a very roughmodel of the human perception of symmetry. It wastherefore infeasible to include symmetry in experiment A,when the aesthetics were measured computationally. Asthe diagrams used in experiment B were created throughinterviews with humans on their perception of thediagrams, it was more appropriate to include symmetry inthis second experiment.1.13 Aesthetic variationIn experiment A, a single control diagram served as amiddle-effect diagram for all the aesthetics. Forexperiment B, a different middle-effect diagram wasproduced for each aesthetic. As the analysis was to bedone with respect to the variations within the aesthetics, itwas not necessary to use the same middle-effect diagramfor all the aesthetics. In experiment A, we did so becauseit was convenient: it was not necessary in experiment B.Thus, for each aesthetic, three diagrams were created byhand: low-effect (-), middle-effect (0) and high-effect (+).To confirm that these diagrams had an appropriateamount of low-, middle- and high-effect of the aesthetics,and that the aesthetics were appropriately controlled,simple perception experiments were performed with 10subjects. These subjects who took part in these perceptiontests were from a comparable subject pool to those whoparticipated in the main experiment.The subjects were asked to rank sets of three diagramsaccording to the presence of the aesthetic. For example, asubject was shown the n+, n0 and n- diagrams and askedto rank them according to the extent of even nodedistribution in the diagrams.In experiment A, we were able to use the computationalmetrics to ensure that there were no possible confounds inthe diagrams. In experiment B, the possible confounds ofsymmetry and orthogonality were also addressed in theinterviews. For example, the subjects were asked to rankthe n+, n0 and n- diagrams according to symmetry, thedesired result being that they would find it difficult to doso. We needed to ensure that a difference in performanceon the node distribution diagrams could not be attributedto differences in symmetry and othogonality.The bends and flow aesthetics were not perceptuallytested in the production of the diagrams, as their presenceis better assessed computationally (for example, bycounting the number of bends or counting the number ofedges pointing upwards). However, the bends and flowdiagrams were tested for the possible symmetry andorthogonality confounds.A total of 10 incorrect diagrams were created byrandomly changing the origin or destination of onerelationship per diagram. The layouts of the falsediagrams were visually comparable to those of the correctdiagrams: as we did not intend to analyse the responses tothe incorrect diagrams, their layout was not important.However, it was, of course, important to include incorrectdiagrams in the experimental set (so that the correctanswer to each diagram presented was not the same), andfor these incorrect diagrams to be visually comparable tothe correct diagrams (so they could not be identified bymere visual pattern matching).The 21 correct and 10 incorrect diagrams were eachpresented once in the online task: a total of 31experimental diagrams.1.14 Results: experiment BBoth the speed and accuracy of the subject’s responsewere measured, enabling the analysis of two differentmeasures of understanding.Average Times051015202530Bends NodeDistribE. Length E.VariationFlow Orthog SymmAesthetic VariationsTime (sec)-0+Aesthetic Accuracy020406080100Bends NodeDistribE. Length E.VariationFlow Orthog SymmAesthetic VariationsAccuracy (%)-0+Figure 4: The response time and accuracy results forexperiment B.Unlike experiment A, some significant accuracy data wasobtained. This was probably because of the reducedtimeout duration (40s rather than 50s), which resulted inmore errors.Using a two-tailed t-test, the statistically significantresults are: Bendso b0 is faster than b- (p < 0.05)o b+ is faster than b- (p < 0.05)o b+ is more accurate than b0 (p = 0.057, approachessignificance) Edge Variationo ev+ is faster than ev0 (p < 0.05)o ev- is faster than ev0 (p < 0.05)o ev+ is more accurate than ev0 (p < 0.05)1.15 Analysis1.15.1 BendsThe results for the bends diagram suggest that a reducednumber of bends produces the best performance. Theaccuracy result (that the diagram with least number ofbends, b+, is more accurate than the middle-effectdiagram, b0), only approaches significance at the 0.05level. This result conforms to our prediction, and previousstudies (Purchase 1997, Purchase et al. 2000).1.15.2 Edge variationThe data show that the middle-effect edge variationdiagram had worse performance than both the diagramwith similar length edges (ev+) and the diagram withedges of greatly varying lengths (ev-) - a result contraryto that of experiment A, when the control diagram had thebest performance.These conflicting edge variation results suggest that thereare other factors to be considered, including the fact thatwe obtained no significant results from the diagramsembodying the edge length or node distributionaesthetics.In the diagrams used in these experiments, no attemptwas made to conform to any semantic grouping; thus thenodes were arbitrarily placed in the diagram. It appearsthat the length of the edges and the spread of the nodesdoes not matter with such positioning. However, it ispossible that performance would be improved if the nodeswere not arbitrarily positioned. For example, if the edgesand nodes were positioned in a manner that placedsemantically related nodes close to each other (even ifthey are not explicitly joined by an edge), performancecould be affected.1.16 DiscussionDespite our efforts to use diagrams that conformed to thehuman perception of aesthetics, rather than acomputational measure, only one of our expectations(with respect to bends) was satisfied in experiment B:five of the aesthetics (node distribution, edge length,symmetry, flow and orthogonality) produced nosignificant results at all, and the significant data from theedge variation aesthetic was difficult to interpret withoutconsidering the possible effects of the semantics of thediagram layout.ConclusionsHaving attempted two versions of this experiment, andobtained few concrete results, it is tempting to say thatnone of the aesthetics really matter (apart from bends,which only matters a little), and therefore there would beno human comprehension differences between two UMLsupport tools that use automatic layout algorithmsembodying different aesthetics.We believe that there are additional semantic issues thatneed to be considered when a layout algorithm is used ina domain-specific tool.Automatic graph layout algorithms typically do not takethe semantics of the diagram into account. As we wishedour results to relate to the design of such algorithms, wedid not consider the semantics of the diagrams when wecreated them according to the layout aesthetics.Our results suggest that improved performance is notmerely related to even node distribution, edge lengths orvariation of the edge lengths, but requires something else:we suggest that the extra feature that needs to beconsidered is the semantic grouping of related objects.Even the surprising results for the bends aesthetics couldbe explained by a break down in semantic grouping thatmay result from eliminating bends entirely: for example,it may be preferable to add some bends to the diagram ifit means that the subclasses in an inheritance hierarchycan be positioned close to each other.This speculation is based on two sources. First, theCognitive Dimensions framework proposed by Green andPetre (1996) includes the dimension of "SecondaryNotation." which is defined as "valuable layout cues[that] are typically not formally part of the notation but can be used to exhibit relationships and structures thatmight otherwise be less accessible" (Petre 1995). Thevisual proximity of objects is a secondary notation: Petre(1995) found that placing unrelated objects next to eachother gave the misleading impression that they weresemantically related. Second, in informal discussions withthe subjects, many of them commented that the groupingof semantically related classes was an important layoutfeature.Further studies could attempt to validate this idea. We canenvisage a similar experiment to the ones described inthis paper, but with the diagrams produced according tovarying levels of semantic grouping. Such an experimentcould help determine the extent to which semanticgrouping is necessary for improved humancomprehension.Another interesting informal comment from the subjectswas related to the nature of the task and the form of theexperimental materials. Students said that they found thediagrams easier to understand if, when reading from topto bottom, the order of the classes matched their order inthe given written specification.This comment demonstrates one of the limitations of thisexperiment. Any formal empirical study has limitations:in our case, we were using university students as subjects,rather than software engineers, and the comprehensiontask and application were constrained to a simple domainand matching task. We chose the task of noticingassociations for which the source or destination wasincorrect as one way of measuring the comprehension ofthe diagram: there are many other ways in whichcomprehension may be assessed, especially in relation toa real-world application task. More extensive case studiesthat follow the use of UML in an industrial application, orthat observe the use of UML support tools in practicewould give a greater insight into suitability of thedifferent aesthetics and the importance of semanticgrouping, from a human comprehension point of view.In choosing a graph layout algorithm to use in a CASEtool, its suitability for comprehension needs to beconsidered. While different generic algorithms,embodying a variety of aesthetics, may produce diagramsthat look attractive, a "nice" layout is unlikely to besufficient for intuitive use. Algorithms that have beenspecifically designed for UML, and which are able to takeinto account the semantics of the diagram, are more likelyto be effective from a human understanding point ofview.AcknowledgementsWe are grateful to the students of the School of ComputerScience and Electrical Engineering at the University ofQueensland who willingly took part in the experiment,and to the Australian Research Council, which fundedthis research. Ethical clearance for this study was grantedby The University of Queensland, 2001.ReferencesCOLEMAN, M. and STOTT PARKER, D. (1996):Aesthetics-based graph layout for human consumption.Software — Practice and Experience 26(12):1415-1438.DI BATTISTA, G., EADES, P., TAMASSIA, I. andTOLLIS, I. (1994): Algorithms for drawing graphs: Anannotated bibliography. Computational Geometry:Theory and Applications 4:235-282.ENTERPRISE ARCHITECHT (2001)http://www.sparxsystems.com.au/ea.htm, 23 October2001.GANSNER, E., and NORTH, D. (1998): Improved force-directed layouts. Proceedings of the Graph DrawingSymposium 1998. Montreal, Canada, 364-373,Springer-Verlag.GREEN, T. and PETRE, M. (1996): Usability analysis ofvisual programming environments: A cognitivedimensions framework. Journal of Visual Languagesand Computing 7:131-174.MICROSOFT VISIO (2001)http://www.microsoft.com/office/visio/, 23 October2001.PAPAKOSTAS, A. and TOLLIS, I. (2000): Efficientorthogonal drawings of high degree graphs.Algorithmica 26(1):100-125.PETRE, M. (1995): Why looking isnt always seeing.Readership skills and graphical programming.Communications of the ACM 38(6):33-44.PURCHASE, H. (1997): Which aesthetic has the greatesteffect on human understanding? Proceedings of theGraph Drawing Symposium 1997, Rome, Italy, 248-261, Springer-Verlag.PURCHASE, H. (2002): Graph drawing aestheticsmetrics. Journal of Visual Languages and Computingto appear.PURCHASE, H., ALLDER, J. and CARRINGTON, D.(2000): User preference of graph layout aesthetics: AUML study. Proceedings of the Graph DrawingSymposium 2000, Colonial Williamsburg, USA, 5-18,Springer-Verlag.PURCHASE, H., COHEN, R. and JAMES, M. (1995):Validating graph drawing aesthetics. Proceedings ofthe Graph Drawing Symposium 1995, Passau,Germany, 435-446, Springer-Verlag.PURCHASE, H., COLPOYS, L. and MCGILL, M.(2001): UML class diagram syntax: An empirical studyof comprehension. Proceedings of the AustralianSymposium on Information Visualisation, Sydney,Australia, this volume.RATIONAL ROSE (2001)http://www.rational.com/products/rose/index.jsp, 23October 2001.RUMBAUGH, J. JACOBSON, I. and BOOCH, G.(1999): The Unified Modeling Language ReferenceManual. Reading, Mass, Addison Wesley LongmanInc.TAMASSIA, A. (1987): On embedding a graph in thegrid with the minimum number of bends. SIAM J.Computing 16(3):421-444.WADDLE, V. (2000): Graph layout for displaying datastructures. Proceedings of the Graph DrawingSymposium 2000, Colonial Williamsburg, USA, 241-252, Springer-Verlag. . Graph drawing aesthetics and the comprehension of UML class diagrams: an empirical study Helen C. Purchase, Matthew McGill, Linda Colpoys and David. certain aesthetic criteria (Coleman and Stott Parker 1996), and claim that by doing so, the resultant graph drawing helps the reader to understand the information
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