An Analysis of Incomplete and Random Financial Networks

Abstract

This paper contributes to the theoretical literature by analyzing the relationship between changes in sparsity and their impacts on financial networks with incomplete and random core-periphery structures, which are widely studied in finance. Sparsity, which measures edge density, reflects the level of connectivity: high sparsity indicates fewer connections between agents, while low sparsity signifies a denser web of interactions. Changes in sparsity result in variations in network impacts. Building on a linear network model inspired by spatial econometrics, we find that reducing sparsity amplifies network impacts in incomplete core-periphery structures through two strategies: 1) increasing the number of core agents and 2) merging two or more core-periphery components. For networks with specific incomplete core-periphery configurations, we derive theoretical results for the average total impact and validate other impact measures through simulations. Furthermore, our analysis extends to networks with randomly generated core-periphery structures, affirming the robustness of our findings.