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Fog computing emerged as a crucial platform for the deployment of IoT applications. The complexity of such applications requires methods that handle the resource diversity and network structure of Fog devices while maximizing the service placement and reducing resource wastage. Prior studies in this domain primarily focused on optimizing specific application requirements and fail to address the network topology combined with the different types of resources encountered in Fog devices. To overcome these problems, we propose a multilayer resource-aware partitioning method to minimize the resource wastage and maximize the service placement and deadline satisfaction rates in a Fog infrastructure with high multi-user application placement requests. Our method represents the heterogeneous Fog resources as a multilayered network graph and partitions them based on network topology and resource features. Afterward, it identifies the appropriate device partitions for placing an application according to its requirements, which need to overlap in the same network topology partition. Simulation results show that our multilayer resource-aware partitioning method is able to place twice as many services, satisfy deadlines for three times as many application requests, and reduce the resource wastage by up to 15-32 times compared to two availability-aware and resource-aware methods.