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IAT 814 Graphs. ______________________________________________________________________________________ SCHOOL OF INTERACTIVE ARTS + TECHNOLOGY [SIAT] | WWW.SIAT.SFU.CA. Graphs. Definition Mathematical structures used to model pairwise relations between objects Example relations - PowerPoint PPT Presentation

PowerPoint Presentation

IAT 8141IAT 814

Graphs______________________________________________________________________________________

SCHOOL OF INTERACTIVE ARTS + TECHNOLOGY [SIAT] | WWW.SIAT.SFU.CA

1Nov 13, 2013IAT 8142GraphsDefinitionMathematical structures used to model pairwise relations between objectsExample relationsAirline FlightsTrain stopsCircles of friends of MyFace2Nov 13, 2013IAT 8143What is a Graph?Vertices (nodes) connected byEdges (links)

123101021013010Adjacency Matrix21312321,32Adjacency List3Nov 13, 2013IAT 8144Graph TerminologyGraphs can have cyclesGraph edges can be directed or undirectedThe degree of a vertex is the number of edges connected to itIn-degree and out-degree for directed graphsGraph edges can have values (weights) on them (nominal, ordinal or quantitative)

21345674Nov 13, 2013IAT 8145TreesSubcase of general graphNo cyclesTypically directed edgesSpecial designated root vertex5Nov 13, 2013IAT 8146Graph UsesIn Information Visualization, any number of data sets can be modeled as a graphTelephone systemWorld Wide WebDistribution network for on-line retailerCall graph of a large software systemSet of connected friends

6Nov 13, 2013IAT 8147Graph Visualization ProblemsGraph layout and positioningMake a concrete rendering of abstract graphScaleNot too much of a problem for small graphs, but large ones are much tougherNavigation/InteractionHow to support user changing focus and moving around the graph

7Nov 13, 2013IAT 8148Scale ChallengeMay run out of space for vertices and edges (turns into ball of string)Can really slow down algorithmOften use clustering to helpExtract highly connected sets of verticesCollapse some vertices together8Nov 13, 2013IAT 8149Navigation/Interaction IssuesHow do we allow a user to query, visit, or move around a graph?Changing focus may entail a different rendering

9Nov 13, 2013IAT 81410Graph UsesFacilitate understanding of complex socioeconomic patternsSocial Science visualization gallery (Lothar Krempel):http://www.mpi-fg-koeln.mpg.de/~lk/netvis.htmlNext slide: Krempel & Plumpers study of World Trade between OECD countries, 1981 and 1992http://www.mpi-fg-koeln.mpg.de/~lk/netvis/trade/WorldTrade.html

10Nov 13, 2013IAT 81411

1981 1992

http://www.mpi-fg-koeln.mpg.de/~lk/netvis/trade/WorldTrade.html11Nov 13, 2013IAT 81412VizsterSocial Network Visualization

Video http://jheer.org/vizster/

12Nov 13, 2013IAT 81413Graph UsesFacilitate understanding of network flows, relationsEven information with a geographical content can best appear as a network rail mapsGeographic landmarks largely suppressed on maps, except water (rivers in Paris, London)13Nov 13, 2013IAT 81414Case StudyAT&T long distance phone network110 Nodes (switches)Geographical locationConnected by 12,000 linksDirected, almost completely connectedData every 5 minutesEARTHQUAKEOct. 17, 1989

14Nov 13, 2013IAT 81415QuestionsWhere are the overloads?Which links are carrying most traffic?Was there network damage?Is there underutilized capacity?Are calls getting in to affected area or are there bottlenecks?Is overload increasing or decreasing?15Nov 13, 2013IAT 81416Edge Drawing Strategies

Label

Thickness

Color

Directed16Nov 13, 2013IAT 81417

17Nov 13, 2013IAT 81418ProblemsToo many lines!OcclusionLong lines become more importantCant see what happens in MidwestSolutionsUse half/half technique out/outDraw most important lastUse thickness & color for traffic

18Nov 13, 2013IAT 81419

19Nov 13, 2013IAT 81420More HelpShorten all lines so as to de-emphasize transcontinental links

20Nov 13, 2013IAT 81421

21Nov 13, 2013IAT 81422Focus of GraphParticular node may be focus, often placed in center for circular layoutHow does one build an interactive system that allows changes in focus?Use animationMaintain constancy of shape, link crossings22Nov 13, 2013IAT 81423Graph LayoutVary hard problem, since graph nodes can have any degreeGood references:Tutorial (talk slides)www.cs.brown.edu/people/rt/papers/gd-tutorial/gd-constraints.pdfG. diBattista, P. Eades, R. Tamassia, and I. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, 1999.Herman et al, IEEE TVCG 2000

23Nov 13, 2013IAT 81424Vertex IssuesShapeColorSizeLocationLabel

24Nov 13, 2013IAT 81425Edge IssuesColorSizeLabelFormPolyline, straight line, orthogonal, grid, curved, planar, upward/downward, ...

25Nov 13, 2013IAT 81426Complexity ConsiderationsCrossings-- minimize towards planarTotal Edge Length-- minimize towards proper scaleArea-- minimize towards efficient use of spaceMaximum Edge Length-- minimize longest edgeUniform Edge Lengths-- minimize variancesTotal Bends minimize orthogonal towards straight-line

26Nov 13, 2013IAT 81427Which Matters?Various studies examined which of the complexity factors matter most and/or what kinds of layout/vis techniques look bestPurchase, Graph Drawing 97Ware et al, Info Vis1(2), June 02Ghoniem et al, Info Vis 4(2), Summer 05Results mixed: Edge crossings seem most important

27Nov 13, 2013IAT 81428Layout HeuristicsLayout algorithms can beplanargrid-basedorthogonalcurved lineshierarchiescircular28Nov 13, 2013IAT 81429Types of Layout AlgorithmsFrom P Mutzel et al Graph Drawing 97

29Nov 13, 2013IAT 81430Layout TypesGrid LayoutPut nodes on a gridTree LayoutSpring LayoutModel graph as set of masses connected by springsPlanar LayoutDetect part of graph that can be laid out without edge crossings30Nov 13, 2013IAT 81431Layout SubproblemsRank AssignmentCompute which nodes have large degree, put those at center of clustersCrossing MinimizationSwap nodes to rearrange edgesSubgraph ExtractionPull out cluster of nodesPlanarizationPull out a set of nodes that can lay out on plane31