WordWalk Puzzle Solving Strategies (Part 4): Indegree and Outdegree of a Graph

In mathematical graph theory, a directed graph is a structure consisting of two sets, a set of vertices and a set of edges.  (In WordWalk we sometimes call these nodes and arrows.)   For any given vertex, we can ask how many edges lead into the vertex and how many lead away from the vertex.  These two numbers have special names in graph theory:

in-degree of a vertex = number of edges (arrows) pointing toward the vertex

out-degree of a vertex = number of edges pointing away from the the vertex.

 In WordWalk, knowing these two numbers can help you make intelligent guesses regarding the likelihood of a given unknown node being one letter vs another.

For instance, the letter E, is very common, and if you look at all the subwords that contain E followed by another letter that should be approximately one less than the out-degree of that node (one less because it may also happen in the unknown rootword).  Likewise, the number of times E is preceded by some other letter should give you an idea of the in-degree of that node.  This can help you decide where the letter E should go.   

Also, since E occurs quite often in English words, you would expect the total number of arrows (i.e., the sum of in-degree and out-degree) to be higher for the E nodes than, say, for the U node (if there is one).

This is a useful hint for solving WordWalk puzzles.

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