Large language model (LLM)-driven agents are designed to handle a wide range of tasks autonomously. As tasks become increasingly composite, the integration of multiple agents into a graph-structured system offers a promising solution. Recent advances mainly architect the communication order among agents into a specified directed acyclic graph, from which a one-by-one execution can be determined by topological sort. However, sequential architectures restrict the diversity of the information flow, hinder parallel computation, and exhibit vulnerabilities to potential backdoor threats. To overcome underlying shortcomings of sequential structures, we propose a node-wise multi-agent scheme, named message passing multi-agent system (MPAS). Specifically, to parallelize the communication across agents, we extend the message propagation mechanism in graph representation learning to multi-agent scenarios and introduce our individual-epistemic message propagation. To further enhance expressiveness and robustness, we investigate three self-driven message aggregators. To achieve desired working flows, collaborative connections can be optimized without constraints. The experimental results reveal that compared to state-of-the-art sequential designs, MPAS could architect more advanced algorithms in 93.8\% of the evaluations, reduce the average communication time from 84.6 seconds to 14.2 seconds per round on AQuA, and improve resilience against backdoor misinformation injection in 94.4\% tests. The code is available at https://anonymous.4open.science/r/MPAS-2E20.