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# Looking for vertex number one

Given an instance of the preferential attachment graph Gn = ([n], En), we would like to find vertex 1, using only ‘local’ information about the graph; that is, by exploring the neighborhoods of small sets of vertices. Borgs et. al gave a O(log^{4} n) algorithm, which is local in the sense that at each step, it needs only search the neighborhood of a set of vertices of size O(log^{4} n). We give a faster algorithm to find vertex 1, which is local in the strongest sense of operating only on neighborhoods of sets of size 1.