The FlowNetwork class represents a capacitated network with vertices named 0 through V - 1, where each directed edge is of type and has a real-valued capacity and flow.

It supports the following two primary operations: add an edge to the network, iterate over all of the edges incident to or from 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 BagItem objects. All operations take constant time (in the worst case) except iterating over the edges incident to a given vertex, which takes time proportional to the number of such edges.