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Abstract

A word network is a set of words of a given length in which any two words differing by only one letter in a single position (such as aunt and runt, or hire and hare) are connected by a line. Using these lines, one can trace out a path leading from any word in a network to any other word in the same network. The terminal words, together with the intermediate words in the path, form a word ladder, well-known since the days of Lewis Caroll (who invented the concept, calling the terminal words doublets and the intermediate words links). There are, of course, many possible word ladders joining any pair of words in a network, but for each pair a minimum-length ladder can be found. If one now considers all pairs of words in the network, one or more of these considers all pairs of words in the network, one or more of these pairs will have a minimum-length ladder that is exceeded in length by no minimum-length ladder belonging to some other pair; that is, these pairs possess the maximum minimum-length word ladders taken over all word-pairs. The number of lines in this maximum path is called the span of the network.

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