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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.
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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 Connectedness Minimum 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.
