Network/graph theory Dr. Chris Davis Postdoc, Faculty of TPM, TU - PowerPoint PPT Presentation

Network/graph theory Dr. Chris Davis Postdoc, Faculty of TPM, TU Delft

Network/graph theory  Network/graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection  Everything is an node or an edge

Vocabulary of graphs Undirected Bi-directional Directed 3.14 Weighted and undirected 3.14 Weighted and directed likes Property graph

Network topology

Measuring networks

Network diameter: longest shortest path Distance 2 4 6 1 2 3 4 5 6 7 1 0 1 1 2 2 1 3 2 1 0 2 1 3 2 4 3 1 2 0 3 1 2 2 1 3 5 4 2 1 3 0 2 1 3 5 2 3 1 2 0 1 1 6 1 2 2 1 1 0 2 Diameter = 4 7 3 4 2 3 1 2 0 7

Average shortest path length  Average number of edges along the shortest paths for all possible pairs of network nodes  Can be considered as a measure of the efficiency of the network

Network topology A B C D E F Strategies to service a set of locations

Topology and network connectivity A C A Average Path Length Fully Connected Network Minimum Network D B B or C D Geographic Barrier Network Length

Path dependent growth: electricity versus gas

Random graphs

Preferentially attached graph

Robustness versus reliability random targeted failures attacks randomly vulnerable robust grown preferentially robust vulnerable grown

Who's in control? You

CA Hidalgo, B Klinger, A-L Barabasi, R Hausmann. The Product Space Conditions the Development of Nations. Science (2007)

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References • Rodrigue, J. P., Comtois, C., & Slack, B. (2013). The geography of transport systems. Routledge. • William Black (2000) “ An Unpopular Essay on Transportation ” , Douglas Fleming lecture, Presented at the meeting of the Association of American Geographers, Pittsburgh, Pennsylvania. • CA Hidalgo, B Klinger, A-L Barabasi, R Hausmann. The Product Space Conditions the Development of Nations. Science (2007)