Network Sparsity and its Impact

We investigate the relationship between sparsity in the weight matrix and network impact. This is the first paper to examine how the sparsity in the weight matrix affects the relationship between the explanatory variable for one agent and the dependent variable in all other agents. We derive the closed-form solution of the relationship between sparsity and network impact under the invariant network topology of sparse network with complete core-periphery components or some specific incomplete core-periphery components. We prove that a reduction in sparsity would increase network impacts under the network structure with complete core-periphery components by three basic approaches of sparsity reduction. For the network with specific incomplete core-periphery
components, we prove the result related to Average Total Impact and show other impacts’ results based on the simulation method. We show the financial network use the simulation method under the network structure with random core-periphery components and arbi