This is one name for a sort of word puzzle which
uses the letters of a set of (usually)
related words as nodes in a directed graph
(with possible loops). Since the puzzle is made for word-puzzle fans and not math-puzzle fans, the nodes are listed individually, along with the set of "next" nodes, rather than by the normal graph diagram.

Suppose we are given the following list of words:

Now we consider each word as a sequence describing a path among letters (for simplicity we ignore letters we don't come across). For example, the word "aardvark" describes the path:

a -> a -> r -> d -> v -> a -> r -> k

So the node a has edges leading to itself and to r; d has an edge leading to v; r has edges leading to d and k; and finally, v has an edge leading to a. The word-puzzle manner of displaying this is

a -> ar
d -> v
r -> dk
v -> a

For a set of strings, as in the example above, we can make a new graph for each word, then take the union of those graphs. Or we can merge as we go. When we do this with the above list of animals, we obtain the following graph:

a -> anrt
b -> a
c -> o
d -> ov
e -> lp
h -> a
l -> e
n -> t
o -> gw
p -> h
r -> dk
v -> a

The challenge for the solver is twofold (but in no particular order): to figure out to what category the words belong, and to determine the complete list of words used to make the puzzle. Notice that unintended words often end up with paths in the final graph; in this example, both 'cog', which is not related to the
category, and 'ant', which is, are valid paths. The puzzle above is not really difficult, because more than half of the nodes are of outdegree 1. Seeing that p leads only to h and h leads only to a and then noticing that only e leads to p should suggest 'elephant' to the average word-puzzler. For a decently difficult puzzle, as few nodes as possible should be of such a low outdegree.

Here is a slightly more difficult puzzle. There are 11 words in the intended word list. Have fun.

a -> irst
c -> alo
d -> ei
e -> dfmnqr
f -> io
i -> cmnot
l -> ael
m -> aemu
n -> it
o -> lnprs
p -> eor
q -> u
r -> emoty
s -> eist
t -> aeiy
u -> al