Given a graph G with n vertices and a bijective labeling of the vertices using the integers 1, 2, . . . , n, we say G has a peak at vertex v if the degree of v is greater than or equal to 2 and if the label on v is larger than the label of all its neighbors. For each subset S ⊂ V(G), we want to determine the number of distinct labelings of the vertices of G such that the vertices in S are precisely the peaks of G. The set S is called the peak set of the graph G, and the set of all labelings with peaks at every vertex in S is denoted by P(S ; G). In this paper, we present an algorithm for constructing all of the labelings in P(S ; G) and explore special cases of peak sets in certain families of graphs, specifically those related to the joins of graphs. We note that this work is a direct generalization of the research of peak sets of permutations, which is the special case when G is the path graph on n vertices.