Data Structures: Weighted Graphs

What is a Weighted Graph?

A Weighted Graph is an abstract data structure that functions as a Graph implementation where all edges are assumed to have weights associated.

What are the operations it requires?

Apart of implementing operations required by Graph abstract data type, following operations are added:

Operation	Arguments	Returns	Description
createEdge	VERTEX, VERTEX, WEIGHT	void	Creates a weighted edge between vertexes along.
isPath	VERTEX, VERTEX	boolean	Checks if there is a path of edges between vertexes.
removeEdge	VERTEX, VERTEX	void	Removes edge between vertexes.

And completes Graph VERTEX with following operations:

Operation	Arguments	Returns	Description
getEdges		EDGES	Gets vertexes current vertex points to in edges.
isEdge	VERTEX	boolean	Checks if current vertex has an edge with that of input
addEdge	VERTEX, WEIGHT	void	Creates a weighted edge between current vertex and that of input
removeEdge	VERTEX	void	Removes edge between current vertex and that of input
setEdgeWeight	VERTEX, WEIGHT	void	Sets weight of edge between current vertex and that of input
getEdgeWeight	VERTEX	WEIGHT	Gets weight of edge between current vertex and that of input

Regarding implementation chosen to store a VERTEX's edges, which reflects into "EDGES" above, following data structures can be used:

Dynamic Array implementing List of VERTEX:WEIGHT pairs: very fast to iterate, very slow to search a value/vertex into. To be used if value inside vertex is not unique!
Hash Table implementing Associative Array where key is VERTEX and value is WEIGHT: quite fast to iterate, very fast to search a value/vertex into. To be used if value inside vertex is unique!

What are the data structures that implement it?

As an abstract data structure, provides only a partial implementation that takes no assumption on whether or not weighted edges are bidirectional or not. It thus needs to be extended by one of below:

Weighted Directed Graph: assumes edges to be unidirectional by default
Weighted Undirected Graph: assumes edges to be always bidirectional