What are valent vertices? Page 13 of Tropical Algebraic Geometry by Itenberg, Mikhalkin, and Shustin mentions 1-valent vertices, but I haven't been able to find a source that actually defines this term or managed to guess the definition myself. Either a definition or reference would be greatly appreciated. Thanks!

In graph theory, the _valency_ of a vertex is sometimes used to mean its _degree_ , i.e. the number of edges incident on it. Both Wikipedia and MathWorld mention both terms as synonyms.