Graph and matrix metrics to analyze ergodic literature for children

What can graph and matrix based mathematical models tell us about ergodic literature? A digraph of storylets connected by links and the corresponding adjacency matrix encoding is used to formulate some queries regarding hypertexts of this type. It is reasoned that the Google random surfer provides a useful model for the behavior of the reader of such fiction. This motivates the use of graph and Web based metrics for ranking storylets and some other tasks. A dataset, termed childif, based on printed books from three series popular with children and young adults and its characteristics are described. Two link-based metrics, SMrank and versions of PageRank, are described and applied on childif to rank storylets. It is shown that several characteristics of these stories can be expressed as and computed with matrix operations. An interpretation of the ranking results is provided. Results on some acyclic digraphs indicate that the rankings convey useful information regarding plot development. In conclusion, using matrix and graph theoretic techniques one can extract useful information from this type of ergodic literature that would be harder to obtain by simply reading it or by examining the underlying digraph.