Internet of Things (IoT) networks have become increasingly characterized by diverse device types, complex partitioned management, and cumbersome security policy configurations. These factors pose significant challenges for fault localization, asset inventory, and security protection within IoT environments. Understanding the network topology of the IoT edge is crucial to addressing these challenges. However, in IoT edge structures, technologies like Network Address Translation (NAT) typically hinder traditional active probing methods from effectively penetrating private networks. In response to this limitation, this paper introduces a novel approach that infers device scale, calculates node correlation coefficients, and determines node relationships, all based on network flow behavior analysis. This approach accurately infers the topology of deep-layer private networks following NAT deployment. The primary objective is to precisely map the topology of deep-layer IoT edge networks. Experimental results demonstrate the exceptional performance of this approach in topology inference, achieving a host device scale metric of 0.8, with link completeness, accuracy, and recall rates of 0.87, 0.84, and 0.73. These results validate the feasibility and effectiveness of the proposed approach, underscoring its capability to accurately infer the topology of deep-layer private network.