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
2
4
6
1
3
5
Diameter = 4
7
Distance
1 2
1 0 1
2 1 0
3 1 2
4 2 1
5 2 3
6 1 2
7 3 4
3
1
2
0
3
1
2
2
4
2
1
3
0
2
1
3
5
2
3
1
2
0
1
1
6
1
2
2
1
1
0
2
7
3
4
2
3
1
2
0
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
B or C
A
C
B
D
D
Geographic Barrier
Network Length
Fully Connected Network
Minimum Network
Average Path Length
A
Path dependent growth:
electricity versus gas
Random graphs
Preferentially attached graph
Robustness versus reliability
random
failures
targeted
attacks
randomly
grown
vulnerable
robust
preferentially
grown
robust
vulnerable
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)