Properties of networks to be considered in their visualization

Jan Terje Bjørke

Networks and graphs

Networks (graphs) are topological structures composed of nodes (vertices) and arcs (links or edges).

The nodes and the arcs have properties which can be classified in several ways.

The classifications used here, points out properties of networks to be considered in their visualization.

Glossary

Graph glossary can be found at

http://www.utm.edu/departments/math/graph/glossary.html

http://www.math.fau.edu/locke/GRAPHTHE.HTM

 

References to graph theory books can be found at http://www.math.fau.edu/locke/Graphstx.htm

 

Graph visualization tools can be found at

http://www.caida.org/tools/visualization/walrus/ http://www.informatik.uni-bremen.de/uDrawGraph/en/

Methodology to identify visual properties of networks

the two (x,y)-coordinates of the plane pixels so small that the visual plane can be regarded

as a subset of R2, metrical and topological properties the variables used to create the image size colour: hue, saturation, value graining direction shape

The embedding space – proposed terminology

• A network is located if all its nodes and links are georeferenced, i.e., positioned on the surface of the earth.

• A network is weak located if only its nodes are georeferenced, i.e., only the end points of its arcs are georeferenced.

• A network is partially located if only some of its nodes or arcs are georeferenced.

• A network is unlocated if it is not georeferenced. 

Properties of the arcs

Directed network

Undirected network

Topological properties

ConnectednessMinimum spanning tree

A network is connected if there is a path connecting every pair of nodes.

A network that is not connected can be divided into disjoint connected subnetworks.

The strength of a network: p =k/(n(n-1))

 

Metrical properties of a network

Shortest path from one node to another.

Travelling salesman route.

 Fuzzy properties

Fuzzy relations

Shape properties – proposed terminology

Networks have shape properties like

list networks

tree networks

arbitrary networks

star networks

Manhattan networks

grid structure.

Visual separation of the elements of a network

The visual separation can be enhanced by generalization operators like displacement, elimination and grouping.

A network has imagined nodes if it not is a planar graph.

 

Degree of generalization

For visualization purposes a subset of nodes or arcs can be mapped into hyper-nodes or hyper-arcs, respectively (see works of F. Bouillé on hypegraph-based data structures, 1977)

Elimination of arcs do not change the number of nodes in the network.

Elimination of nodes reduces the number of arcs in the network.

 

Oslo

24% eliminated

43% eliminated

49% eliminated

Research questions

• How do people perceive networks?• How is their ability to remember networks?• How do people recognize patterns in networks and what type of

patterns do they look for?• Develop algorithms to compute the layout of the network in the

image plane that maximizes the visual clarity of the network.

The unlocated network has a degree of freedom that can be used to enhance its shape properties.

JTB-Networks-october2005.doc