Before revision:  Finally, we also study persistent Laplacians for a filtration of simplicial complexes, and present interesting stability results for their eigenvalues  .
After revision:  Finally, we also study persistent Laplacians for a filtration of simplicial complexes, and present interesting stability results for their eigenvalues . Our work brings methods from spectral graph theory, circuit theory, and persistent homology together with a topological view of the combinatorial Laplacian on simplicial complexes .