The SymbolGraph class represents an undirected graph, where the vertex names are arbitrary strings. By providing mappings between string vertex names and integers, it serves as a wrapper around the data type, which assumes the vertex names are integers between 0 and V - 1. It also supports initializing a symbol graph from a file.

This implementation uses an to map from strings to integers, an array to map from integers to strings, and a to store the underlying graph. The Index and Contains operations take time proportional to log V, where V is the number of vertices. The Name operation takes constant time.