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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 a very high clustering coefficient, but
significant low average pathlength, e.g. by 1) forming a ring of
vertices, 2) placing a central vertex in the middle of the ring and 3)
connecting each vertice of the ring with this central vertex. The
average pathlength of this network is about 2, whereas the clustering
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!
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