Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of language tasks, yet complex multi-step reasoning remains a fundamental challenge. While Large Reasoning Models (LRMs) equipped with extended chain-of-thought mechanisms demonstrate improved performance over standard LLMs, both model types still suffer from accuracy collapse on sufficiently complex tasks, suggesting that scaling model-level reasoning alone is insufficient. Inspired by the global workspace theory of human cognition, we propose Brain-Inspired Graph Multi-Agent Systems (BIGMAS), in which specialized LLM agents are organized as nodes in a dynamically constructed directed graph and coordinate exclusively through a centralized shared workspace. A problem-adaptive GraphDesigner constructs task-specific agent topologies, while a global Orchestrator leverages the complete shared state for routing decisions, overcoming the local-view bottleneck of reactive approaches. Experiments on Game24, Six Fives, and Tower of London across six frontier LLMs demonstrate that BIGMAS consistently improves reasoning performance for both standard LLMs and LRMs, outperforming existing multi-agent baselines including ReAct and Tree of Thoughts, showing that multi-agent architectural design provides complementary gains orthogonal to model-level reasoning enhancements.