# Graph & Network Analysis

Mathematica provides state-of-the-art functionality for analyzing and synthesizing graphs and networks. Building on Mathematica's powerful numerical and symbolic capabilities, Mathematica 8 brings numerous high-level functions for computing with graphs.

• Modern extensible platform for graph computation and network analysis. »
• Support for directed, undirected, and weighted graphs.
• Hundreds of built-in Mathematica functions and standard graph algorithms.
• Direct support for random graph distributions. »
• Extensive collection of graph operations and modifications. »
• Support for set-theoretic and Boolean-based operations on graphs. »
• Selection of graph elements and subgraphs using Mathematica pattern language.
• Comprehensive collection of predicates for testing graph properties. »
• Efficient graph isomorphism testing. »
• Local and global structural properties, including components, covers, and matchings.
• 15+ metrics and centrality measures to characterize graphs and networks. »
• Efficient shortest path, cycle, and navigation functions. »
• Multi-paradigm approach to graph programming with matrix, optimization, and Boolean-based frameworks. »
• Generic BFS and DFS algorithms with a flexible programmatic interface. »
• Support of arbitrary properties for graph elements.
• Full integration of graphs and networks into Mathematica.
 Study Urban Road Networks » London Underground » Solve Mazes » Analyze Random Graph Models » Vertex Degree Distributions » Analyze Social Networks » Symbolic Computation on Graphs  » Subtract Random Neighborhoods » Test Properties » Convert to Matrix Representations » Find an Isomorphism » Degree Centrality in Social Networks » Compute the Betweenness Centrality » Centrality in Citation Networks » Center, Periphery, and Distance Functions » Visualize Eulerian Cycles » Visualize Hamiltonian Cycles » Color Cycle Decompositions » Topological Sorting » Shortest Paths » Solve the Icosian Game » Trip Planning » Find K-Core Components » Highlight Strongly Connected Components » Find In- and Out-Components » Edge Covers » Independent Edge Sets  » Highlight BFS and DFS trees » Perform a Breadth-First Scan » Perform a Depth-First Scan » Study Properties of a Directed Graph » Study Properties of an Undirected Graph » Analyze Large and Complex Networks »