Recent speaker diarization studies showed that integration of end-to-end neural diarization (EEND) and clustering-based diarization is a promising approach for achieving state-of-the-art performance on various tasks. Such an approach first divides an observed signal into fixed-length segments, then performs {\it segment-level} local diarization based on an EEND module, and merges the segment-level results via clustering to form a final global diarization result. The segmentation is done to limit the number of speakers in each segment since the current EEND cannot handle a large number of speakers. In this paper, we argue that such an approach involving the segmentation has several issues; for example, it inevitably faces a dilemma that larger segment sizes increase both the context available for enhancing the performance and the number of speakers for the local EEND module to handle. To resolve such a problem, this paper proposes a novel framework that performs diarization without segmentation. However, it can still handle challenging data containing many speakers and a significant amount of overlapping speech. The proposed method can take an entire meeting for inference and perform {\it utterance-by-utterance} diarization that clusters utterance activities in terms of speakers. To this end, we leverage a neural network training scheme called Graph-PIT proposed recently for neural source separation. Experiments with simulated active-meeting-like data and CALLHOME data show the superiority of the proposed approach over the conventional methods.