2. Consider the random graph G(n, p) with average degree c. (a) Show that in the limit of large n the expected number of triangles in the network is 1 6 c 3 . In other words, show that the number of triangles is constant, neither growing nor vanishing in the limit of large n. (b) Show that the expected number of connected triples in the network is 1 2 nc2 (c) Hence, calculate the clustering coefficient C, as defined in the lecture notes, and confirm that it agrees for large n with the value given in the slides (i.e. C = c n1 )