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

Mar 31, 2024 •456 likes •643 views

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

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)
Thank you for your attention! Please post any questions you may have on our discussion forum
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)

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