Question: Consider the maximum entropy ensemble for the Erd ?os-R ´enyi random graph model P(G; ß), as discussed in class. Compute the Shannon entropy S[P] = S(ß) of this ensemble as a function of ß and N. As a function of ß for what ß is the entropy maximum and what is its maximum value? Interpret your result. Can you write an expression for S(ß) for the general case with arbitrary constraints x = (x1, . . . , xK), using the free energy and perhaps its derivatives?