cis 467/602-01: data visualizationdkoop/cis467/lectures/lecture13.pdf · cis 467, spring 2015 cis...

CIS 467, Spring 2015

CIS 467/602-01: Data Visualization

Networks

Dr. David Koop

Assignment 2• http://www.cis.umassd.edu/

~dkoop/cis467/assignment2.html • Scaling width • Text elements and selectAll • Any other questions? • Allow submissions until 11:59pm

tonight

2CIS 467, Spring 2015

http://www.cis.umassd.edu/~dkoop/cis467/assignment2.html

Exam (Next Wednesday)• Topics

- Everything in book and lectures through and including networks - HTML, CSS, SVG, JavaScript, and D3 Concepts

• Format - Multiple-choice - Free response questions - Graduate students will have extra questions


Arrange Tables

Express Values

Separate, Order, Align Regions

Axis Orientation

Layout Density

Dense Space-Filling

Separate Order Align

1 Key 2 Keys 3 Keys Many KeysList Recursive SubdivisionVolumeMatrix

Rectilinear Parallel Radial

Recap (Arrange Tables)


[Munzner (ill. Maguire), 2014]

Recap (Loading Data)• CSV, TSV, XML, JSON • D3’s asynchronous methods to load data • Cars Example


Networks• Why not graphs?

- Bar graph - Graphing functions in mathematics - Nodes and edges connecting the nodes

• Network: nodes and edges connecting the nodes • Formally, G = (V,E) is a set of nodes V and a set of edges E where

each edge connects two nodes. • Nodes == items, edges connect items • Both nodes and edges may have attributes


Node–Link Diagrams

Enclosure

Adjacency Matrix

TREESNETWORKS

Connection Marks

TREESNETWORKS

Derived Table

TREESNETWORKS

Containment Marks

Arrange Networks and Trees


[Munzner (ill. Maguire), 2014]

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Molecule Graph


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Molecule Graph


•Nodes may have attributes (e.g. element)

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Molecule Graph


•Nodes may have attributes (e.g. element)

•Edges may have attributes(e.g. number of bonds)

Web Sites as Graphs (amazon.com)


[M. Salathe, 2006]

Social Networks


[P. Butler, 2010]

Graphs as Data


ID Atom Electrons Protons0 N 7 71 C 6 62 S 16 163 C 6 64 N 7 7

ID1 ID2 Bonds0 1 11 2 11 3 23 4 1

Nodes

Edges

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Node-Link Diagrams• Data: nodes and edges • Task: understand connectivity,

paths, structure (topology) • Encoding: nodes as point marks,

connections as line marks • Scalability: hundreds

• …but high density of links can be problematic!

• Problem with the above encoding?


Arc Diagram


[D. Eppstein, 2013]

Network Layout• Need to use spatial position when designing network visualizations • Otherwise, nodes can occlude each other, links hard to distinguish • How?

- With bar charts, we could order using an attribute… - With networks, we want to be able to see connectivity and

topology (not in the data usually) • Possible metrics:

- Edge crossings - Node overlaps - Total area


Force-Directed Layout• Nodes push away from each other

but edges are springs that pull them together

• Weakness: nondeterminism, algorithm may produce difference results each time it runs


[M. Bostock, 2012]

sfdp


[Hu, 2005]

“Hairball”


[Hu, 2014]

Adjacency Matrix• Change network to tabular data

and use a matrix representation • Derived data: nodes are keys,

edges are boolean values • Task: lookup connections, find well-

connected clusters • Scalability: millions of edges

• Can encode edge weight, too


ii

ii

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7.1. Using Space 135

Figure 7.5: Comparing matrix and node-link views of a five-node network.a) Matrix view. b) Node-link view. From [Henry et al. 07], Figure 3b and3a. (Permission needed.)

the number of available pixels per cell; typically only a few levels wouldbe distinguishable between the largest and the smallest cell size. Networkmatrix views can also show weighted networks, where each link has an as-sociated quantitative value attribute, by encoding with an ordered channelsuch as color luminance or size.

For undirected networks where links are symmetric, only half of thematrix needs to be shown, above or below the diagonal, because a linkfrom node A to node B necessarily implies a link from B to A. For directednetworks, the full square matrix has meaning, because links can be asym-metric. Figure 7.5 shows a simple example of an undirected network, witha matrix view of the five-node dataset in Figure 7.5a and a correspondingnode-link view in Figure 7.5b.

Matrix views of networks can achieve very high information density, upto a limit of one thousand nodes and one million edges, just like clusterheatmaps and all other matrix views that uses small area marks.

Technique network matrix viewData Types networkDerived Data table: network nodes as keys, link status between two

nodes as valuesView Comp. space: area marks in 2D matrix alignmentScalability nodes: 1K

edges: 1M

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.1.3.3 Multiple Keys: Partition and Subdivide When a dataset has onlyone key, then it is straightforward to use that key to separate into one region

[Henry et al., 2007]

Cliques in Adjacency Matrices


[Gehlenborg and Wong]

Structures from Adjacency Matrices


[McGuffin]

Node-Link or Adjacency Matrix?• Empirical study: For most tasks, node-link is better for small graphs

and adjacency better for large graphs • Multi-link paths are hard with adjacency matrices • Immediate connectivity or neighbors are ok, estimating size (nodes

& edges also ok) • People tend to be more familiar with node-link diagrams • Link density is a problem with node-link but not with adjacency

matrices


Trees• A tree is a directed, acyclic graph

- Directed: edges are oriented - Acyclic: once you follow an edge from a node, you’ll never come

back to that same node • Trees have a root node and parent-child edges


cis 467/602-01: data visualizationdkoop/cis467/lectures/lecture13.pdf · cis 467, spring 2015 cis...

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