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Some graph statistics (and Matlab tools)

CS240A: Classes of Graphs and Their Properties slides under construction – see the Matlab transcript for what I actually did in class. Some graph statistics (and Matlab tools). Vertex degree histogram: dhist.m Avg shortest path length or BFS level profile: bfslevels.m

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Some graph statistics (and Matlab tools)

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  1. CS240A: Classes of Graphsand Their Propertiesslides under construction – see the Matlab transcript for what I actually did in class

  2. Some graph statistics (and Matlab tools) • Vertex degree histogram: dhist.m • Avg shortest path length or BFS level profile: bfslevels.m • Clustering coefficient: ccoeff.m • c = 3*(# triangles) / (# connected triples) • Laplacian eigenvalues (and vectors): meshpart toolbox • Separator size: meshpart toolbox • Fill (chordal completion size): analyze.m and amd.m

  3. Some classes of graphs • Graphs observed in the wild (see Florida collection for many examples): • Finite element meshes: CGmats.m • Circuit simulation graphs: circuit_3.mat • Relationship networks: coAuthorsDBLP.mat, PGPgiantcompo.mat • … many others! • Classifications of graphs: • Power-law graphs • Small-world graphs • Planar graphs • Overlap graphs • Generators for classes of graphs: • Erdos-Renyi (flat) random graphs: sprandsym.m • RMAT random graph generator: rmat.m • 2-D and 3-D mesh generators: grid5.m etc. in meshpart toolbox

  4. RMAT Approximate Power-Law Graph

  5. Strongly Connected Components

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