The Graph class represents an undirected graph of vertices named 0 through V - 1. It supports the following two primary operations: add an edge to the graph, iterate over all of the vertices adjacent to a vertex. It also provides methods for returning the number of vertices V and the number of edges E. Parallel edges and self-loops are permitted.

This implementation uses an adjacency-lists representation, which is a vertex-indexed array of objects. All operations take constant time (in the worst case) except iterating over the vertices adjacent to a given vertex, which takes time proportional to the number of such vertices.