Multi-agent debate has proven effective in improving large language models quality for reasoning and factuality tasks. While various role-playing strategies in multi-agent debates have been explored, in terms of the communication among agents, existing approaches adopt a brute force algorithm – each agent can communicate with all other agents. In this paper, we systematically investigate the effect of communication connectivity in multi-agent systems. Our experiments on GPT and Mistral models reveal that multi-agent debates leveraging sparse communication topology can achieve comparable or superior performance while significantly reducing computational costs. Furthermore, we extend the multi-agent debate framework to multi-modal reasoning and alignment labeling tasks, showcasing its broad applicability and effectiveness. Our findings underscore the importance of communication connectivity on enhancing the efficiency and effectiveness of the “society of minds” approach.