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.

翻译：本研究关注复杂网络，即具有嵌入动力系统的底层图结构。我们旨在减少网络中的边数，同时最小化对网络动力学的影响。提出一种算法框架，可在无向图的反应扩散复杂系统上生成稀疏图（即边数较少的图）。将稀疏化问题形式化为降阶模型空间（ROM空间）上的数据同化问题，并结合约束条件以保持拉普拉斯矩阵在扰动下（L = D - A，其中D为度对角矩阵，A为邻接矩阵）的特征模态。提出近似方法用于求解拉普拉斯矩阵受扰动时的特征值与特征向量。通过在多个真实世界图上的实验验证了该方法的有效性。