Problem 1. In an ErdsRnyi graph with N=4000 nodes, the linking probability is p=0.001 a) What is the average degree of a node in this graph? b) What is the variance in the degrees of the nodes? c) What is the expected number of nodes with a degree which is at least twice larger than the average degree? Problem 2. Consider Gn,p, an ErdsRnyi random graph with n nodes, m edges, and mean degree c: a) Compute the probability p of creating an edge in Gn,p. b) Show that in the limit (large n) the expected number of triangles in Gn,p is 1/6 c 3

Problem 1. In an ErdsRnyi graph with N=4000 nodes, the linking probability is p=0.001 a) What is the average degree of a node in this graph? b) What is the variance in the degrees of the nodes? c) What is the expected number of nodes with a degree which is at least twice larger that the average degree? Problem 2. Consider Gnp, an Erds-Rnyi random graph with n nodes, medges, and mean degree c: a) Compute the probability p of creating an edge in Gn.p. b) Show that in the limit (large n) the expected number of triangles in Gmp is 1/ 6c Problem 1. In an ErdsRnyi graph with N=4000 nodes, the linking probability is p=0.001 a) What is the average degree of a node in this graph? b) What is the variance in the degrees of the nodes? c) What is the expected number of nodes with a degree which is at least twice larger that the average degree? Problem 2. Consider Gnp, an Erds-Rnyi random graph with n nodes, medges, and mean degree c: a) Compute the probability p of creating an edge in Gn.p. b) Show that in the limit (large n) the expected number of triangles in Gmp is 1/ 6c