network/graph theory - edx
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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
021324372011221611021325312031242213021342312012312211017654321
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)