Is there any JavaScript libraries for graph operations and algorithms?

What I need is a JavaScript implementation of pure mathematical graphs. To be clear I DON'T mean graph visualization libraries like sigma.js or d3.js.

The library I'm looking for would implement following features:

• creation of directed and undirected graph objects
• creation of weighted and unweighted graps objects
• adding/removing vertices and edges to/from the graph
• adding labels to vertices and edges (i.e. additional meta data)
• implementation of basic graph search and traversal algorithms like depth-first-search, breadth-first search, Dijkstra's algorithm, A* and others.

Does anyone know if one already exists?

Now there is a library: graphlib

Graphlib is a JavaScript library that provides data structures for undirected and directed multi-graphs along with algorithms that can be used with them.

Implements:

• directed and undirected graphs (does A -> B imply B -> A)
• multigraphs (multiple distinct named edges from A -> B)
• compound graphs (nodes can have children that form a "subgraph")
• Dijkstra algorithm (shortest path)
• Floyd-Warshall algorithm (shortest path supporting negative weights)
• Prim's algorithm (minimum spanning tree)
• Tarjan's algorithm (strongly connected components)
• Topological sorting (dependency sort for directed acyclic graphs)
• Pre- and postorder traversal (callback on every node)
• Finding all cycles and testing if a graph is acyclic
• Finding all connected components

NPM, Bower and browser supported, MIT license.