Data assimilation for sparsification of reaction diffusion systems in a complex network

The study focuses on complex networks that are underlying graphs with an embedded dynamical system. We aim to reduce the number of edges in the network while minimizing its impact on network dynamics. We present an algorithmic framework that produces sparse graphs meaning graphs with fewer edges on reaction-diffusion complex systems on undirected graphs. We formulate the sparsification problem as a data assimilation problem on a Reduced order model space(ROM) space along with constraints targeted towards preserving the eigenmodes of the Laplacian matrix under perturbations(L = D - A, where D is the diagonal matrix of degrees and A is the adjacency matrix of the graph). We propose approximations for finding the eigenvalues and eigenvectors of the Laplacian matrix subject to perturbations. We demonstrate the effectiveness of our approach on several real-world graphs.