  To improve the reasoning and question-answering capabilities of Large
Language Models (LLMs), several multi-agent approaches have been introduced.
While these methods enhance performance, the application of collective
intelligence-based approaches to complex network structures and the dynamics of
agent interactions remain underexplored. This work extends the concept of
multi-agent debate to more general network topologies, measuring the
question-answering accuracy, influence, consensus, and the effects of bias on
the collective. The results show that random networks perform similarly to
fully connected networks despite using significantly fewer tokens. Furthermore,
a strong consensus among agents correlates with correct answers, whereas
divided responses typically indicate incorrect answers. Analysing the influence
of the agents reveals a balance between self-reflection and interconnectedness;
self-reflection aids when local interactions are incorrect, and local
interactions aid when the agent itself is incorrect. Additionally, bias plays a
strong role in system performance with correctly biased hub nodes boosting
performance. These insights suggest that using random networks or scale-free
networks with knowledgeable agents placed in central positions can enhance the
overall question-answering performance of multi-agent systems.
