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# Small-world networks [3 P]

Carry out a web search and find three datasets that have small-world properties. That is

1. the cluster coefficient should be at least 20% larger than for corresponding random networks that consist of the same number of elements.
2. the average shortest path length should differ at most by 10% compared to random networks.
Use MATLAB to calculate the cluster coefficient and the average shortest path length of the networks. Hints:
a)
Use the commands fopen, fclose, textscan, textread and sscanf to read data files in MATLAB (type HELP for details).
b)
Write a function that takes the connectivity matrix as input and calculates the cluster coefficient and the average shortest path length.
c)
To calculate the cluster coefficient count only links between existing neighbors. Nodes with only one or zero links are therefore not used for the calculation. This is a property of undirected graphs. If necessary you can convert a directed graph into an unidirected one.
d)
To calculate the average shortest path length ignore unconnected nodes and average only over shortest path lengths of connected nodes. This is a property of directed and undirected graphs.
e)
For each dataset that represents a directed graph you can choose if you analyse the original directed graph or its undirected version obtained by adding reciprocal links.
f)
You can start your web search at http://www-personal.umich.edu/ mejn/netdata/.
Present your results clearly, structured and legible. Document them in such a way that anybody can reproduce them effortless.

Next: Robustness [3 P] Up: MLB_Exercises_2008 Previous: Patterning [5+4* P]
Haeusler Stefan 2009-01-19