Pathlengths of small-world networks

[funkwecker]

Hi,
i have a question this hopefully fits into the scope of this forum.
Small-world networks are characterised by a higher clustering coefficient and comparable or slightly higher average pathlength than the one's of random networks with same number of edges and vertices (see Watts & Strogatz famous paper in nature).
However, it is easy to construct a network with very high clustering coefficient, but significantly low average pathlengt, e.g. 1) form a ring of vertices, 2) place a central vertice in the middle of the ring and connect each vertice with this central vertice. The average pathlength of this network is about 2, whereas the clusterign coefficient is nearly 1.

So, my questions:
a) Is a network with high clustering coefficent and low path length (lower than the one of a random network) still a small-world network?
b) Is there some more precise definition of small-world networks?

Thank you very much!

[seinecle]

Hi,

For these kind of questions I think you will get better chances of getting answers if you post them on the mailing list of SOCNET:
http://www.insna.org/pubs/socnet.html

This is a lively list for those interested in network analysis in general. On the Gephi forum you are more likely to find advice on Gephi-specific issues.

Best,

Clement

[funkwecker]

Thank you very much for this hint. I will give it a try there.