H517 Visualization Design, Analysis, & Evaluation Week 11: - - PowerPoint PPT Presentation

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H517 Visualization Design, Analysis, & Evaluation Week 11: Networks & Trees Khairi Reda | redak@iu.edu School of Informa5cs & Compu5ng, IUPUI Last week Small Multiples Nick Elprin, Domino Multi form Based on a slide by Miriam

SLIDE 1

H517 Visualization Design, Analysis, & Evaluation

Khairi Reda | redak@iu.edu School of Informa5cs & Compu5ng, IUPUI

Week 11: Networks & Trees

SLIDE 2

Last week…

SLIDE 3

Small Multiples

Nick Elprin, Domino

SLIDE 4

Multi form

Based on a slide by Miriam Meyer and Alex Lex

SLIDE 5

networks tables

friendship network

SLIDE 6

cnn.com wired.com apple.com

Websites as networks of pages

Via Miriah Meyer

SLIDE 7

Network (aka Graph)

V: Set of ver5ces (or nodes) E: Set of edges An edge e = (x, y) connects two ver5ces x and y For example:

V = {1, 2, 3, 4} E = {(1,2), (1, 4), (3, 2), (3, 4)}

1 2 3 4 1 4 3 2 1 2 3 4

Node-link diagram

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Graph terminology

Via Miriah Meyer

trees

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Graph vs. Tree

Graph

Nodes and edges No constraint on edges

Tree

Parents and children No “loops”

Hierarchical

rganizational

structures

Genome / phenotype similarity (tree of life)

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Node-Link Diagram

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Node-Link Diagram

http://bl.ocks.org/mbostock/4063550

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Limita5ons

Tree breadth tend to grow exponen5ally
Quickly run out of space!
Solu5ons
Scrolling or panning
Collapsing nodes
Hyperbolic layouts

Based on a slide by Miriah Meyer

Hyperbolic layout

Node-Link tree diagrams

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Icicle Plot

C A B F X Y Z D E

D E A B C F X Y Z

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Icicle Plot

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Radial Icicle Plot

http://bl.ocks.org/mbostock/raw/4348373/

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IndentaKon

Place all items along ver5cal

paced rows

Indenta5on used to show parent/

child rela5onships

Commonly used as a component

in user interfaces (e.g., File Explorer, Finder)

OUen requires significant

scrolling

Based on a slide by Miriah Meyer

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Enclosure Diagrams

Encode structure using spa5al enclosure
OUen referred to as a treemap
Pros
Provides single view of en5re tree
Easier to spot small/large branches
Cons
Difficult to interpret depth

Based on a slide by Miriah Meyer

C A B D E

A B C D E

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Treemap

http://homes.cs.washington.edu/~jheer//files/zoo/

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Treemap

Disk Inventory X

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Graph vs. Tree

Graph

Nodes and edges No constraint on edges

Tree

Parents and children No “loops”

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Visualizing Graphs

Node-link layouts
Force-Directed layout
A[ribute-based
Adjacency matrices
Aggregate Views
Mo5f Glyphs
PivotGraph

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Node-link diagrams

Primary concern of graph drawing is layout
f nodes (and ul5mately the edges)
Goal is to effecKvely depict the overall

graph structure

Connec5vity, path following
Clusters
Key readability measure: reduce the

frequency of edge crossing

1 2 3 4 1 4 3 2

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Exercise

create an aesthe5cally pleasing node-link diagram for this network

Miriah Meyer

SLIDE 24

Exercise

Miriah Meyer

create an aesthe5cally pleasing node-link diagram for this network

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Force-directed layout

Physical model
Nodes = repulsive par5cles
Edges = springs

Miriah Meyer

SLIDE 26

http://bl.ocks.org/mbostock/4062045

Force-directed layout

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Force-directed layout

Many varia5ons, but usually physical analogy:
Repulsion force: fR(d) = CR * m1*m2 / d2
m1, m2 are node masses
d is distance between nodes
AUracKon force: fA(d) = CA * (d – L)
L is the rest length of the spring
Total force on a node x with posi5on x’

∑ neighbors(x) : fA(||x’-y’||) * (x’-y’) + -fR(||x’-y’||) * (x’-y’)

Miriah Meyer

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Force-directed layout

Start from a random layout
Loop (top-level):
For every node pair, compute repulsive force
For every node pair, compute a[rac5ve force
accumulate forces per node
update each node posi5on in direc5on of

accumulated force

stop when layout is ‘good enough’

Miriah Meyer

Algorithm

SLIDE 29

https://bl.ocks.org/mbostock/1062288

Collapsable force-directed graphs

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The internet

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Force-directed layout

Pros
Flexible, aesthe5cally pleasing layouts on many

types of graphs

Can add custom forces
Rela5vely easy to implement
Cons
Computa5onally expensive O(n3) for a non-
p5mized implementa5on
Prone to local minima

Based on a slide by Miriah Meyer

SLIDE 32

Node-link diagram

Based on a slide by Miriah Meyer

Pros
Intui5ve visual mapping
Can show overall structure,

clusters, and paths

Cons
Not good for dense graphs (the

hairball problem)

SLIDE 33

Visualizing Graphs

Node-link layouts
Force-Directed layout
A[ribute-based
Adjacency matrices
Aggregate Views
Mo5f Glyphs
PivotGraph

SLIDE 34

Adjacency Matrix

Miriah Meyer

SLIDE 35

Adjacency Matrix

https://bost.ocks.org/mike/miserables/

SLIDE 36

Pros
Good for dense graphs
Visually scalable
Highlights clusters
Cons
Not as intui5ve, compared to a graph
Row/column order affects percep5on of pa[erns
Hard to follow paths

Adjacency Matrix

SLIDE 37

Hybrid: node-link + matrix

NodeTrix, Henry and Fekete, 2007

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Visualizing Graphs

Node-link layouts
Force-Directed layout
A[ribute-based
Adjacency matrices
Aggregate Views
Mo5f Glyphs
PivotGraph

SLIDE 39

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MoKf Glyphs

Dunne 2013

connector fan clique

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MoKf Glyphs

Dunne 2013

SLIDE 42

MoKf Glyphs

Dunne 2013