We present a deep-learning approach for earthquake detection using waveforms from a seismic array consisting of multiple seismographs. Although automated, deep-learning earthquake detection techniques have recently been developed at the single-station level, they have potential difficulty in reducing false detections owing to the presence of local noise inherent to each station. Here, we propose a deep-learning-based approach to efficiently analyze the waveforms observed by a seismic array, whereby we employ convolutional neural networks in conjunction with graph partitioning to group the waveforms from seismic stations within the array. We then apply the proposed method to waveform data recorded by a dense, local seismic array in the regional seismograph network around the Tokyo metropolitan area, Japan. Our method detects more than $97$ percent of the local seismicity catalogue, with less than $4$ percent false positive rate, based on an optimal threshold value of the output earthquake probability of $0.61$. A comparison with conventional deep-learning-based detectors demonstrates that our method yields fewer false detections for a given true earthquake detection rate. Furthermore, the current method exhibits the robustness to poor-quality data and/or data that are missing at several stations within the array. Synthetic tests demonstrate that the present method has the potential to detect earthquakes even when half of the normally available seismic data are missing. We apply the proposed method to analyze 1-hour-long continuous waveforms and identify new seismic events with extremely low signal-to-noise ratios that are not listed in existing catalogs. (241words)