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The clustering coefficient for erdos renyi model $G(n,p) = p$.

Now i have been studying in various papers that it cannot model real world networks which has high clustering coefficient. My question is that if we use a higher probability value for the model then we our clustering coefficient should increase then why cant we use this model for such real world networks like small world phenomenon ?

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  • $\begingroup$ Side remark: for Geometric Random Graph clustering coefficient is known and depend only on dimension of space: en.wikipedia.org/wiki/… $\endgroup$ May 22, 2020 at 16:34
  • $\begingroup$ What could that mean intuatively? $\endgroup$ May 22, 2020 at 16:39

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In an ER graph, density and clustering coefficient are equal. In most "real-world networks", they differ by orders of magnitude.

Therefore, if an ER graph has a realistic density, then it has not a realistic clustering coefficient; and if it has a realistic clustering coefficient, then it has not a realistic density.

This is actually a key element that makes ER graphs poor models for most real-world networks: in practice, despite a low density, the clustering coefficient if high. You are right in pointing the fact that a high clustering coefficient alone is easy to obtain.

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