Speaker identification in the household scenario (e.g., for smart speakers) is typically based on only a few enrollment utterances but a much larger set of unlabeled data, suggesting semisupervised learning to improve speaker profiles. We propose a graph-based semi-supervised learning approach for speaker identification in the household scenario, to leverage the unlabeled speech samples. In contrast to most of the works in speaker recognition that focus on speaker-discriminative embeddings, this work focuses on speaker label inference (scoring). Given a pre-trained embedding extractor, graph-based learning allows us to integrate information about both labeled and unlabeled utterances. Considering each utterance as a graph node, we represent pairwise utterance similarity scores as edge weights. Graphs are constructed per household, and speaker identities are propagated to unlabeled nodes to optimize a global consistency criterion. We show in experiments on the VoxCeleb dataset that this approach makes effective use of unlabeled data and improves speaker identification accuracy compared to two state-of-the-art scoring methods as well as their semi-supervised variants based on pseudo-labels.