1. Consider the Erds-Rnyi random graphs G(n,p) with mean degree 5. (a) Show that in the...

 

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1. Consider the Erds-Rnyi random graphs G(n,p) with mean degree 5. (a) Show that in the limit of large n the expected number of triangles in the network is 63. (b) The clustering coefficient C is given as follows (Eq. 7.41 in Newman's book): C = 3x number of triangles number of connected triples i. Show that the expected number of connected triples in the network is no. ii. Calculate the clustering coefficient C according to this definition (using the above results), and confirm that it agrees for large n with the value given by C = n-1 1. Consider the Erds-Rnyi random graphs G(n,p) with mean degree 5. (a) Show that in the limit of large n the expected number of triangles in the network is 63. (b) The clustering coefficient C is given as follows (Eq. 7.41 in Newman's book): C = 3x number of triangles number of connected triples i. Show that the expected number of connected triples in the network is no. ii. Calculate the clustering coefficient C according to this definition (using the above results), and confirm that it agrees for large n with the value given by C = n-1