Natural Language Generation has been rapidly developing with the advent of large language models (LLMs). While their usage has sparked significant attention from the general public, it is important for readers to be aware when a piece of text is LLM-generated. This has brought about the need for building models that enable automated LLM-generated text detection, with the aim of mitigating potential negative outcomes of such content. Existing LLM-generated detectors show competitive performances in telling apart LLM-generated and human-written text, but this performance is likely to deteriorate when paraphrased texts are considered. In this study, we devise a new data collection strategy to collect Human & LLM Paraphrase Collection (HLPC), a first-of-its-kind dataset that incorporates human-written texts and paraphrases, as well as LLM-generated texts and paraphrases. With the aim of understanding the effects of human-written paraphrases on the performance of state-of-the-art LLM-generated text detectors OpenAI RoBERTa and watermark detectors, we perform classification experiments that incorporate human-written paraphrases, watermarked and non-watermarked LLM-generated documents from GPT and OPT, and LLM-generated paraphrases from DIPPER and BART. The results show that the inclusion of human-written paraphrases has a significant impact of LLM-generated detector performance, promoting TPR@1%FPR with a possible trade-off of AUROC and accuracy.