Graph-tool is an efficient Python module for manipulation and statistical analysis of graphs (a.k.a. networks). Contrary to most other python modules with similar functionality, the core data structures and algorithms are implemented in C++, making extensive use of template metaprogramming, based heavily on the Boost Graph Library. This confers it a level of performance that is comparable (both in memory usage and computation time) to that of a pure C/C++ library.
Despite its nice, soft outer appearance of a regular python module, the core algorithms and data structures of graph-tool are written in C++, with performance in mind. Most of the time, you can expect the algorithms to run just as fast as if graph-tool were a pure C/C++ library. See a performance comparison.
Many algorithms are implemented in parallel using OpenMP, which provides excellent performance on multi-core architectures, without degrading it on single-core machines.
An extensive array of features is included, such as support for arbitrary vertex, edge or graph properties, efficient "on the fly" filtering of vertices and edges, powerful graph I/O using the GraphML, GML and dot file formats, graph pickling, graph statistics (degree/property histogram, vertex correlations, average shortest distance, etc.), centrality measures, standard topological algorithms (isomorphism, minimum spanning tree, connected components, dominator tree, maximum flow, etc.), generation of random graphs with arbitrary degrees and correlations, detection of modules and communities via statistical inference, and much more.
Conveniently draw your graphs, using a variety of algorithms and output formats (including to the screen). Graph-tool has its own layout algorithms and versatile, interactive drawing routines based on cairo and GTK+, but it can also work as a very comfortable interface to the excellent graphviz package.
Every single function in the module is documented in the docstrings and in the online documentation, which is full of examples.