瓜 (melon) and 葛 (kudzu vine) are both climbing plants whose vines tangle together. Tangled vines = tangled connections between people.
usage
瓜葛 often implies an unwanted or suspicious connection. Common patterns: 有瓜葛 (have connections), 没有瓜葛 (no involvement), 撇清瓜葛 (distance oneself from connections).
