The reverie of the network is referred to here. The reverie was about the brief meeting with the girl who boarded the train at Rohana. The narrator was daydreaming about his short and sweet interaction with the girl and how they exchanged views on various topics like the beauty of the hills in October, The view of the landscape from the train’s window, etc. The narrator felt that the brief encounter would stay with him for a long time.
The male passenger who boarded the train at Saharanpur broke into the narrator’s reverie by saying that he is not nearly as attractive a travelling companion as the one who just left.