Complex Systems 535/Physics 508: Homework 4 Because of Fall Break, you have two weeks to do this homework. It is due in class on Tuesday, October 27. 1. Consider the random graph G(n, p). (i) Show that in the limit of large n the expected number of triangles in the network is 16c3, where c is the mean degree. In other words, the number of triangles is con- stant, neither growing nor vanishing in the limit of large n. (ii) Show that the expected number of connected triples in the network (as in Eq. (7.41)) i s 21 n c 2 . (iii) HencecalculatetheclusteringcoefficientC,asdefinedinEq.(7.41),andconfirmthat it agrees for large n with the value given in Eq. (12.11)