Given a symmetric real matrix, how does the pattern of zero and nonzero off-diagonal entries affect the possible eigenvalues? In particular, given a specified pattern, what is the maximum multiplicity of an eigenvalue in any matrix with that pattern? To answer this question, we associate a simple graph to every pattern according to the graph's adjacency matrix. A parameter called the zero forcing number of this graph helps us bound the the maximum multiplicity of an eigenvalue; we define and begin to explore this parameter.