Lecture20

# Lecture20 - Connectivity: Directed network Trees Hierarchic...

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1 Geography 12: Maps and Spatial Reasoning Lecture 20: Network Maps Professor Keith Clarke On-line Street Map London Underground Trams in Melbourne, Australia

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2 Airline Routes Power Grid Terminology of networks • Topology • Link or route • Place or node • Topological distance •D iame te r
3 Fully connected planar graph Fully connected non-planar graph Non-planar graph Graph Theory n = # nodes • Planar graph/Non-planar • Symmetric/ Non-symmetric (one-way, two-way) • Symmetric planar maximum # connections is: 3(n – 2) • Symmetric non-planar maximum # connections is: [n (n – 1)] /2 • Non-symmetric non-planar maximum # connections is: n (n – 1) • Non-symmetric planar maximum # connections is: 6 (n – 2)

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4 Graph measures Nodes 7 Links 7 Diameter 3 Max possible links 3 (n – 2) = 15 Connectivity index (actual vs. possible) 100A/P = 47% 3 2 3 2 2 3 3 LA Metro Rail network Netvizz on facebook Distortion
5 Directed graph

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Unformatted text preview: Connectivity: Directed network Trees Hierarchic order Strahler stream order Bifurcation ratio: ratio of links at one order to links at the next order Street network: Pruning 6 Stream order Strahler order in GIS http://www.krisweb.com/krisredwoodck/krisdb/html/krisweb/maps/order_ortho.gif Panama: Streams from SRTM Terrain: stream network 7 National Hydrographic Database Distance to network Connections between networks: SkyWest: Spoke and hub Directions: MapQuest 8 Shortest path: Dijkstras algorithm Visit all nodes, shortest path Robert Kosara: EagerEyes.org Isochrone Voronoi diagram 9 Voronoi World Population (equal cells) Network maps Terminology from topology: node, link, directed, planar Simple measures possible e.g. diameter, connectivity index Tree networks have orders, e.g. Strahler and measures e.g. branching ratio Algorithms can compute shortest path Isochrones...
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## This note was uploaded on 12/27/2011 for the course GEOG 12 taught by Professor Gautier during the Fall '08 term at UCSB.

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Lecture20 - Connectivity: Directed network Trees Hierarchic...

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