As 6G approaches, the proliferation of large language models (LLMs) and embodied intelligence is driving a paradigm shift from the Internet of Things (IoT) to the Internet of Agents (IoA). However, traditional network architectures, designed for content-agnostic data transmission, struggle to accommodate the bursty, reasoning-driven traffic patterns and rigorous multimodal synchronization requirements of autonomous agents. This paper surveys the AI-agent communication network (ACN), aiming to bridge the gap between static network resources and dynamic agent tasks. We analyze the evolution from bit-oriented transmission to agentic syntax protocols, which enable intent-based signaling and semantic compression. Furthermore, we explore mechanisms for multi-agent collaborative consensus and distributed decision-making under the constraints of unstable wireless environments. We critically focus on task-driven dynamic networking, examining how integrated sensing, communication, and computing (ISCC) and network-embedded agents (NEA) facilitate the real-time generation of task graphs and intent-aware traffic scheduling. To synthesize these technologies, we propose a reference framework, the Deep-Agentic Network Architecture (DAN-Arch), which vertically integrates physical-layer sensing with application-layer reasoning flows. Finally, open challenges regarding energy efficiency, cross-domain governance, and 3GPP standardization pathways are discussed to guide future research towards a fully agent-native 6G ecosystem.