Network/graph theory

Dr. Chris DavisPostdoc, 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

Undirected

Bi-directional

Directed

Weighted and undirected

Weighted and directed

Property graphlikes

3.14

3.14

Vocabulary of graphs

Network topology

Measuring networks

Network diameter: longest shortest path

1

2

3

4

5

6

7Diameter = 4

Distance

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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

A B C

D E F

Network topology

Strategies to service a set of locations

Topology and network connectivity

Ave

rag

e P

ath

Len

gth

Network Length

Min

imu

m N

etw

ork

Fu

lly C

on

nec

ted

Net

wo

rk

Geographic Barrier

A

B or C

D

A

B

C

D

Path dependent growth: electricity versus gas

Random graphs

Preferentially attached graph

vulnerable

robust

randomlygrown

preferentiallygrown

randomfailures

robust

vulnerable

targetedattacks

Robustness versus reliability

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)