Apart from branching narratives, as commonly found in Choose Your Own Adventure books and in interactive fiction, there is no necessarily obvious way to convert a narrative into a network: unless, of course, what one has mind is a rather thin narrative in which every node only has a relationship to the node before it and the node after it, which is entirely possible, but not all that interesting. That doesn’t mean there aren’t a variety of ways to derive networks from narratives, but they are, as the verb recognizes, derivative, though often quite compelling.
The first way that most analysts turned to was to re-create studies of actual social networks in fictional social networks: determining the relationship between characters was either something done by hand, based on the insight of the analyst, or something automated: if two characters appeared in the same scene in a dramatic work or the same page or scene or chapter in a novel, then they could be said to be connected. The depth or nature of the link was something that could either be qualified or quantified: e.g., the more scenes two characters appeared in together, the stronger the link between the two. This simple method offered some unusual insights. In one study of Greek and Irish mythic narratives, the analysts found that the social networks in the Irish narratives were more like actual social narratives than those found in the Greek narratives.
I have never seen such a network inverted, so that events are connected by the number of characters they have in common, but someone must have done it, and I wonder what it revealed?
Another method for deriving a network from a narrative is to determine all the locations involved and to map them and then create a network of where characters travel or what happens at those locations.