Rox its an open source framework for building Graph-based applications. It has been built essentially for academic jobs, such as graph algorithm execution and theorem proofs.

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This project its split in two main cores: The Graph API, that have been developed to provide to users the ability to work with graphs without necessarily a graphical user interface. And the Graphical User Interface, based on Eclipse RCP, that provides the ability to either edit graphs trough a specific editor for Graph files and execute algorithms.

Main Features

• Extensible Graph API
• Supports Simple Graphs, Directed Graphs, Trees, MultiGraphs, PseudoGraphs, and what kind of graph you want (just extend!)
• Supports algorithm execution
• Easy-to-use graphical interface

How does it works?

...and what it has that make it different from the others

The whole software is plugin-based, what means that everything you do (like new algorithms implementations or new node types) can be shared among other users and/or be attached to the main stream version of the framework. This portal, indeed, was built for that purpose, to be a information exchange site on graph theory algorithms and its applications.
The RoxGT its basically a set of eclipse plugins that can be used together so you will not worry about to create and (most important) to validate the whole graph structure to model your specific problem.

Is it open source?

...and how you can join us

Nowadays the framework is hosted on java.net under Eclipse Public License (EPL).

What is Graph Theory?

...and how things are related to it

Extracted from http://en.wikipedia.org/wiki/Graph_theory

In mathematics and computer science, graph theory has for its subject matter the properties of graphs. Informally speaking, a graph is a set of objects called points or vertices connected by links called lines or edges. In a graph proper, which is by default undirected, a line from point A to point B is considered to be the same thing as a line from point B to point A. In a digraph, short for directed graph, the two directions are counted as being distinct arcs or directed edges.

Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be represented by graphs. The link structure of a website could be represented by a directed graph: the vertices are the web pages available at the website and there's a directed edge from page A to page B if and only if A contains a link to B. The development of algorithms to handle graphs is therefore of major interest in computer science.

A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road¹. Another way to extend basic graphs is by making the edges to the graph directional (A links to B, but B does not necessarily link to A, as in webpages), technically called a directed graph or digraph. A digraph with weighted edges is called a network.

Networks have many uses in the practical side of graph theory, network analysis (for example, to model and analyze traffic networks or to discover the shape of the internet -- see Applications below). Within network analysis, the definition of the term "network" varies, and may often refer to a simple graph