Affiliation: | a Linguistics Department, University of California Santa Cruz, Santa Cruz, CA 95064, United Statesb Department of Mathematics, Juniata College, Huntingdon, PA 16652, United Statesc Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, United Statesd Computer Science Department, Naval Postgraduate School, Monterey, CA 93943, United States |
Abstract: | Linguists often represent the relationships between words in a collection of text as an undirected graph G=(V,E), where V is the vocabulary and vertices are adjacent in G if and only if the words that they represent co-occur in a relevant pattern in the text. Ideally, the words with similar meanings give rise to the vertices of a component of the graph. However, many words have several distinct meanings, preventing components from characterizing distinct semantic fields. This paper examines how the structural properties of triangular line graphs motivate the use of a clustering coefficient on the triangular line graph, thereby helping to identify polysemous words. The triangular line graph of G, denoted by T(G), is the subgraph of the line graph of G where two vertices are adjacent if the corresponding edges in G belong to a K3. |