Lecture 3

Question 1

Graph

Answer 1

A graph refers to a set of vertices (nodes) and a set of edges (i.e. links) that connect pairs of vertices.

Question 2

Tree

Answer 2

a tree is a graph in which any two vertices are connected by exactly one path. Alternatively, any connected graph with no cycles is a tree.

Question 3

Graph density

Answer 3

Number of edges |E| relative to the maximum potential number of edges

Question 4

How to reduce the size of a graph?

Answer 4

• Topological properties: Remove nodes with small number of connections (edges).
• Random removal
• Representative based: Geodesic clustering by finding a set of representative vertices such that the geodesic (shortest path) distance for all elements to such a representative is minimized. Poor representative is in outer boundary and far removed from the others.
• Based on connectedness: Remove edges such that any two connected vertices remain connected

Question 5

Answer 5

Think about it.

Question 6

Spanning trees

Answer 6

Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree connecting all vertices.

Question 7

Pathfinder networks

Answer 7

In the final graph all paths between two nodes form shortest paths.

Question 8

Graph aggregation (or hierarchical clustering methods)

Answer 8

In this approach, nodes and edges are merged to single nodes and edges, thereby reducing the size of the graph and revealing relationships between groups of nodes.

Question 9

Planarity

Answer 9

the ability to draw connected data nodes with no crossing edges

Question 10

General extensions to graph drawing (aesthetic criteria)

Answer 10

• Reduce visual clutter
• Reduce spatial aliases
• Spatial matching of multiple representatives
• Maximize compactness

Question 11

Dynamic extensions (3)

Answer 11

• Preserving the mental map
• Reducing the cognitive load
• Minimizing temporal aliases

Question 12

Graphs: predictability property

Answer 12

Two different runs on same algorithm should yield identical results.

Potential problem is that some algorithms use random initialization.

Question 13

Force based layouts

what is spring-mass based algorithm?

what does it try to optimize?

Answer 13

Graph uses attraction and repulsion forces. Nodes that are connected to each other by an edge have attractive forces and vice versa. The forces bring connected nodes closer.

Uniform edge length

Symmetry

Question 14

Three algorithms for force based layouts?

Answer 14

EADES: Electric force for repulsion and spring force for attraction

KAMADA AND KAWAI: Desirable distance is proportional to the length of the shortest path between nodes

FRUCHTERMAN AND REINGOLD: Improves EADES distribution of nodes

Question 15

Node-link vs adjacency matrix diagram

how do they perform in terms of the 4 characteristics?

Answer 15

Reduce visual clutter: Visual clutter that is caused in the node-link approach by lots of edge crossings is here reduced to a minimum in matrices.

Reduce spatial aliases: This problem can happen in both. It might be hard to differentiate two adjacent columns or rows. Or two edges might cross in very small angles.

Spatial matching of multiple representatives: With matrices it is tough. User has to toggle between row and columns to follow edges.

Maximize compactness: Matrix representation can be very compact at each cell can be reduced to a single pixel.

Question 16

Visual encoding idioms for a tree

Answer 16

A: rectilinear vertical node‐link
B: rectangular horizontal node‐link C: Icicle
D: Radial node‐link
E: Concentric circles (sunburst)
F: Nested circles
G: Treemap
H: Indented outline

Question 17

Edge bundling

• What is it for?
• What is it?
• What are the advantages?

Answer 17

• Datasets with both child-parent and adjacency relations.
• We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another.
• This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques.

Question 18

Enclosure

Answer 18

Uses containment marks for hierarchical structures.