1. Network Vis. 1.1 Motivation Examples for networks and graph related data � � Molecular and genetic maps, biochemical pathways 1. (Multivariate) Network � Object-oriented systems and data structures, scene graphs Visualization (VRML) � Real-time systems (state diagrams) � Semantic networks and knowledge representation diagrams Information Visualization (186.141) � Project management (PERT diagrams) or documentation TU Vienna, Austria management June 13 & 14, 2013 � VLSI � … ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren DV – Prof. Dr. Andreas Kerren 2 1. Network Vis. 1. Network Vis. 1.2 Definitions 1.2 Definitions Graphs are abstract structures, that can be used for Terminology � � modeling relational information � Graphs can have cycles Graph G = ( V , E ) � � Edges can be directed or undirected � V : Set of nodes (objects) � E : Set of edges connecting nodes (relation) � The degree of a node is the number of edges that are � Data structures: connected with this node � At directed graphs � In-degree is the number of the incoming edges � Out-degree is the number of the outgoing edges Graph Drawing: automatic drawing of � Edges can have values (edge weights) with different types � graphs in 2D and 3D ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren 3 DV – Prof. Dr. Andreas Kerren 4 1. Network Vis. 1. Network Vis. 1.2 Definitions 1.2 Definitions Types of graphs Types of graphs (cont.) � � � Trees � Directed/Undirected graphs � Properties � Extended graph models � Special case of a graph � Hierarchical graphs � No cycles � Special root node � Clustered graphs � Free trees � Hypergraphs � Binary trees � … � Root trees � Ordered trees � Planar graphs ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 5 6 DV – Prof. Dr. Andreas Kerren DV – Prof. Dr. Andreas Kerren 1

1. Network Vis. 1. Network Vis. 1.3 Graph Drawing 1.3 Graph Drawing Research areas of GD (cont.) Own research community � � � Navigation in large graphs ⇒ very large field! � Dynamic graphs � I can only give an overview � Heterogeneous node and edge types � A good starting point for literature search and further � Massive node degrees information are the annual Graph Drawing conferences ( GD ) � Visualization of isomorphic subgraphs or the IEEE InfoVis conferences (Embedding of additional information) � Research areas of GD � (Focus & Context) � � Graph layout and positioning of nodes (Comparison of graphs) � � … � Scalability ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren 7 DV – Prof. Dr. Andreas Kerren 8 1. Network Vis. 1. Network Vis. 1.3 Graph Drawing 1.3 Graph Drawing Drawing Conventions Independent from layout and interaction techniques, � � there are many different possibilities to draw nodes and � Polyline Drawing edges � Straight-line Drawing � Orthogonal Drawing � Nodes � Grid Drawing � Shape, color, size, position, label, … � Planar Drawing � Edges � Upward Drawing � Color, size, thickness, direction, label, … � Shape � Circular Drawing � straight, curved, planar, orthogonal, … � … [Inspired by S. Hong und P. Eades‘ course] ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren 9 DV – Prof. Dr. Andreas Kerren 10 1. Network Vis. 1. Network Vis. 1.3.1 Aesthetics 1.3.1 Aesthetics 1.3 Graph Drawing 1.3 Graph Drawing A graph layout should be easy to read and to � All layout algorithms fulfill more or less a set of � understand, easy to remember, as well as have a aesthetics criteria certain aesthetics Furthermore, the layout itself affects the perception of � graphs Problem: These aesthetics criteria are sometimes � contradictory are their computation mostly NP hard! Thus, the most GD algorithms are heuristics � [taken from S. Hong und P. Eades‘ course] [taken from S. Hong und P. Eades‘ course] ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 11 12 DV – Prof. Dr. Andreas Kerren DV – Prof. Dr. Andreas Kerren 2

1. Network Vis. 1. Network Vis. 1.3.1 Aesthetics 1.3.1 Aesthetics 1.3 Graph Drawing 1.3 Graph Drawing Example: crossings and bends Aesthetics Criteria � � Edge crossings ↓ � Area ↓ � Symmetry ↑ � Edge length ↓ � Maximal edge length, uniform edge length, total edge length � Bends of edges ↓ � Maximal bends, uniform bends, total bends � Resolution ↑ [taken from S. Hong und P. Eades‘ course] ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren 13 DV – Prof. Dr. Andreas Kerren 14 1. Network Vis. 1. Network Vis. 1.3.1 Aesthetics 1.3.2 Force-directed GD 1.3 Graph Drawing 1.3 Graph Drawing Example: Conflict between two criteria Force-directed methods model nodes and edges as � � physical objects Examples � � Spring forces for the edges � Gravitation forces for the nodes Aim is to find a stable configuration, that gets by with as � few energy as possible We have here also optimization problems, that are � solved locally [taken from S. Hong und P. Eades‘ course] ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 DV – Prof. Dr. Andreas Kerren 15 DV – Prof. Dr. Andreas Kerren 16 1. Network Vis. 1. Network Vis. 1.3.2 Force-directed GD 1.3.2 Force-directed GD 1.3 Graph Drawing 1.3 Graph Drawing Spring Embedder Problems of the classic Spring Embedder algorithm is � the high runtime and its (possibly) breakdown with very Firstly presented by P. Eades, 1984 � large graphs Approach realizes two criteria � Layout example: � Symmetry � � Uniform edge lengths [taken from S. Hong und P. Eades‘ course] ISOVIS ISOVIS Linnaeus University Erasmus Teaching Exchange 13 Linnaeus University Erasmus Teaching Exchange 13 17 18 DV – Prof. Dr. Andreas Kerren DV – Prof. Dr. Andreas Kerren 3

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