The analysis of axillary and supraclavicular lymph nodes is a primary prognostic factor for the staging of breast cancer. However, due to the size of lymph nodes and the low resolution of PET data, their segmentation is challenging. We investigate the relevance of considering axillary and supraclavicular lymph node segmentation from PET/CT images by coupling Convolutional Neural Networks (CNNs) and Component-Trees (C-Trees). Building upon the U-Net architecture, we propose a framework that couples a multi-modal U-Net fed with PET and CT, coupled with a hierarchical model obtained from the PET that provides additional high-level region-based features as input channels. Our working hypotheses are twofold. First, we take advantage of both anatomical information from CT for detecting the nodes, and from functional information from PET for detecting the pathological ones. Second, we consider region-based attributes extracted from C-Tree analysis of 3D PET/CT images to improve the CNN segmentation. We carried out experiments on a dataset of 240 pathological lymph nodes from 52 patients scans, and compared our outputs with human expert-defined ground-truth, leading to promising results.