INTRODUCTION TO GRAPH DRAWING Fall 2010 Battista G

INTRODUCTION TO GRAPH DRAWING Fall 2010 Battista, G. D. , Eades, P. , Tamassia, R. , and Tollis, I. G. 1998 Graph Drawing: Algorithms for the Visualization of Graphs. 1 st. Prentice Hall PTR.

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WHAT ARE GRAPHS A vertices and relationships, set of entities, vertices edge between those entities. edges s

TERMINOLOGY • • 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

TRANSITIVE REDUCTION

ADJACENCY MATRIX AND ADJACENCY LIST

DRAWING OF A GRAPH

Connected graph Cutvertex Biconnected graph Block of a graph

WE NEED … Graph …. Combinatorial properties � � � Directed Acyclic …

PARAMETERS OF GRAPH DRAWING METHODS Drawing conventions Aesthetics Constraints Efficiency

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

AESTHETICS 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

CONSTRAINTS 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

PRECEDENCE 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 crossing Maximize 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