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Efficient and robust online processing technique of irregularly structured data is crucial in the current era of data abundance. In this paper, we propose a graph/network version of the classical adaptive Sign algorithm for online graph signal estimation under impulsive noise. Recently introduced graph adaptive least mean squares algorithm is unstable under non-Gaussian impulsive noise and has high computational complexity. The Graph-Sign algorithm proposed in this work is based on the minimum dispersion criterion and therefore impulsive noise does not hinder its estimation quality. Unlike the recently proposed graph adaptive least mean p-th power algorithm, our Graph-Sign algorithm can operate without prior knowledge of the noise distribution. The proposed Graph-Sign algorithm has a faster run time because of its low computational complexity compared to the existing adaptive graph signal processing algorithms. Experimenting on steady-state and time-varying graph signals estimation utilizing spectral properties of bandlimitedness and sampling, the Graph-Sign algorithm demonstrates fast, stable, and robust graph signal estimation performance under impulsive noise modeled by alpha stable, Cauchy, Student's t, or Laplace distributions.