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Video highlight detection is a crucial yet challenging problem that aims to identify the interesting moments in untrimmed videos. The key to this task lies in effective video representations that jointly pursue two goals, \textit{i.e.}, cross-modal representation learning and fine-grained feature discrimination. In this paper, these two challenges are tackled by not only enriching intra-modality and cross-modality relations for representation modeling but also shaping the features in a discriminative manner. Our proposed method mainly leverages the intra-modality encoding and cross-modality co-occurrence encoding for fully representation modeling. Specifically, intra-modality encoding augments the modality-wise features and dampens irrelevant modality via within-modality relation learning in both audio and visual signals. Meanwhile, cross-modality co-occurrence encoding focuses on the co-occurrence inter-modality relations and selectively captures effective information among multi-modality. The multi-modal representation is further enhanced by the global information abstracted from the local context. In addition, we enlarge the discriminative power of feature embedding with a hard-pairs guided contrastive learning (HPCL) scheme. A hard-pairs sampling strategy is further employed to mine the hard samples for improving feature discrimination in HPCL. Extensive experiments conducted on two benchmarks demonstrate the effectiveness and superiority of our proposed methods compared to other state-of-the-art methods.