This paper explores a new outlier detection algorithm based on the spectrum of the Laplacian matrix of a graph. Taking advantage of boosting together with sparse-data based learners. The sparcity of the Laplacian matrix significantly decreases the computational burden, enabling a spectrum based outlier detection method to be applied to larger datasets compared to spectral clustering. The method is competitive on synthetic datasets with commonly used outlier detection algorithms like Isolation Forest and Local Outlier Factor.