Application Areas

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 »
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