This paper investigates the impact of sparse communication topology on the effectiveness and efficiency of multi-agent debate (MAD) frameworks. The authors explore how reducing the number of reference solutions visible to each agent can improve performance while significantly reducing computational costs. Experiments on GPT and Mistral models show that sparse MAD can achieve comparable or superior performance on reasoning tasks such as MATH and MathVista, with a reduction in input token costs of up to 40%. The framework is also extended to multimodal reasoning and alignment labeling tasks, demonstrating its broad applicability. The study finds that sparse MAD allows for more rounds of effective debate, leading to better performance. Additionally, assigning stronger LLMs to more connected agents enhances overall performance. The paper concludes by highlighting the importance of communication topology in improving the efficiency and effectiveness of multi-agent systems.This paper investigates the impact of sparse communication topology on the effectiveness and efficiency of multi-agent debate (MAD) frameworks. The authors explore how reducing the number of reference solutions visible to each agent can improve performance while significantly reducing computational costs. Experiments on GPT and Mistral models show that sparse MAD can achieve comparable or superior performance on reasoning tasks such as MATH and MathVista, with a reduction in input token costs of up to 40%. The framework is also extended to multimodal reasoning and alignment labeling tasks, demonstrating its broad applicability. The study finds that sparse MAD allows for more rounds of effective debate, leading to better performance. Additionally, assigning stronger LLMs to more connected agents enhances overall performance. The paper concludes by highlighting the importance of communication topology in improving the efficiency and effectiveness of multi-agent systems.