I NTRODUCTION TO G RAPH DRAWING Fall 2010 Battista, G. D., Eades, P., Tamassia, R., and Tollis, I. G. 1998 Graph Drawing: Algorithms for the Visualization.

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Presentation transcript:

I NTRODUCTION TO G RAPH DRAWING Fall 2010 Battista, G. D., Eades, P., Tamassia, R., and Tollis, I. G Graph Drawing: Algorithms for the Visualization of Graphs. 1st. Prentice Hall PTR.

W HAT ARE GRAPHS A set of entities, vertices and relationships, edges between those entities. vertices edges

T ERMINOLOGY E is a finite multiset of edges or unordered pairs of (u,v) Self-loop Multiple edge Simple graph End vertices Adjacent Incident

Degree of vertex Directed edge Digraph Directed edge Indegree, Outdegree Incomming edge Outgoing edge

T RANSITIVE R EDUCTION

A DJACENCY MATRIX AND A DJACENCY LIST

D RAWING OF A GRAPH

Connected graph Cutvertex Biconnected graph Block of a graph

W E NEED … Graph …. Combinatorial properties Directed Acyclic …

P ARAMETERS OF GRAPH DRAWING METHODS Drawing conventions Aesthetics Constraints Efficiency

D RAWING CONVENTIONS Polyline drawing Straight-line drawing Orthogonal drawing Grid drawing Planar drawing Upward (downward) drawing (PERT ( Program Evaluation Review Technique)) Drawing conventions Aesthetics Constraints Efficiency

A ESTHETICS Crossing edges Area of drawing Total edge length Maximum edge length Uniform edge length Total bend Maximum bend Uniform bend Angular resolution Aspect ratio Symmetry Drawing conventions Aesthetics Constraints Efficiency

C ONSTRAINTS Center the given vertex External the given vertex Cluster the given subset of vertices Left-right (top-bottom) Shape (predefined) Drawing conventions Aesthetics Constraints Efficiency

P RECEDENCE AMONG AESTHETICS Aesthetics often conflict with each other so some tradeoffs are unavoidable Even if they do not conflict it is algorithmically hard to deal with them at the same time Minimize edge crossingMaximize symmetry

APPROACHES The topology-shape-metrics approach Planarization Orthogonalization Compaction The hierarchical approach Layer assignment Crossing reduction X-coordinate assignment The visibility approach Planarization Visibility Replacement The augmentation approach Planarization Augmentation Triangulation drawing The Force-directed approach The divide and conquer approach