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We present the fastest FPRAS for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence $(d_i)_{i=1}^n$ with maximum degree $d_{\max}=O(m^{1/4-\tau})$, our algorithm generates almost uniform random graph with that degree sequence in time O(mdmax) where is the number of edges in the graph and 茂戮驴is any positive constant. The fastest known FPRAS for this problem [22] has running time of O(m3n2). Our method also gives an independent proof of McKay's estimate [33] for the number of such graphs.Our approach is based on sequential importance sampling(SIS) technique that has been recently successful for counting graphs [15,11,10]. Unfortunately validity of the SIS method is only known through simulations and our work together with [10] are the first results that analyze the performance of this method.Moreover, we show that for d= O(n1/2 茂戮驴 茂戮驴), our algorithm can generate an asymptotically uniform d-regular graph. Our results are improving the previous bound of d= O(n1/3 茂戮驴 茂戮驴) due to Kim and Vu [30] for regular graphs.