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

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

Mar 31, 2024 456 likes •646 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

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Network/graph theory

  • Dr. Chris Davis

Postdoc, Faculty of TPM, TU Delft

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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

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Undirected Bi-directional Directed Weighted and undirected Weighted and directed Property graph

likes 3.14 3.14

Vocabulary of graphs

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Network topology

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Measuring networks

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Network diameter: longest shortest path

1 2 3 4 5 6 7

Diameter = 4 Distance 2 1 3 2 4 3 7 2 1 1 2 2 1 6 1 1 2 1 3 2 5 3 1 2 3 1 2 4 2 2 1 3 2 1 3 4 2 3 1 2 1 2 3 1 2 2 1 1 1 7 6 5 4 3 2 1

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  • 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

Average shortest path length

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A B C D E F

Network topology

Strategies to service a set of locations

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Topology and network connectivity

Average Path Length Network Length

Minimum Network Fully Connected Network Geographic Barrier

A B or C D A B C D

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Path dependent growth: electricity versus gas

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Random graphs

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Preferentially attached graph

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vulnerable robust

randomly grown preferentially grown random failures

robust vulnerable

targeted attacks

Robustness versus reliability

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Who's in control?

You

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

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Thank you for your attention!

Please post any questions you may have

  • n our discussion forum
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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)