How to effectively incorporate cross-utterance information cues into a neural language model (LM) has emerged as one of the intriguing issues for automatic speech recognition (ASR). Existing research efforts on improving conualization of an LM typically regard previous utterances as a sequence of additional input and may fail to capture complex global structural dependencies among these utterances. In view of this, we in this paper seek to represent the historical con information of an utterance as graph-structured data so as to distill cross-utterances, global word interaction relationships. To this end, we apply a graph convolutional network (GCN) on the resulting graph to obtain the corresponding GCN embeddings of historical words. GCN has recently found its versatile applications in social-network analysis, summarization, and among others due mainly to its ability of effectively capturing rich relational information among elements. However, GCN remains largely underexplored in the con of ASR, especially for dealing with conversational speech. In addition, we frame ASR N-best reranking as a prediction problem, leveraging bidirectional encoder representations from transformers (BERT) as the vehicle to not only seize the local intrinsic word regularity patterns inherent in a candidate hypothesis but also incorporate the cross-utterance, historical word interaction cues distilled by GCN for promoting performance. Extensive experiments conducted on the AMI benchmark dataset seem to confirm the pragmatic utility of our methods, in relation to some current top-of-the-line methods.