In this paper, we propose an effective and robust method for acoustic scene analysis based on spatial information extracted from partially synchronized and/or closely located distributed microphones. In the proposed method, to extract spatial information from distributed microphones while taking into account whether any pairs of microphones are synchronized and/or closely located, we derive a new cepstrum feature utilizing a graph-based basis transformation. Specifically, in the proposed graph-based cepstrum, the logarithm of the amplitude in a multichannel observation is converted to a feature vector by an inverse graph Fourier transform, which can consider whether any pair of microphones is connected. Our experimental results indicate that the proposed graph-based cepstrum effectively extracts spatial information with consideration of the microphone connections. Moreover, the results show that the proposed method more robustly classifies acoustic scenes than conventional spatial features when the observed sounds have a large synchronization mismatch between partially synchronized microphone groups.