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

- the
*cluster coefficient*should be at least 20% larger than for corresponding random networks that consist of the same number of elements. - the
*average shortest path length*should differ at most by 10% compared to random networks.

- 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/`.