CS240A: Classes of Graphs and Their Properties slides under construction – see the Matlab transcript for what I actually did in class.

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Presentation transcript:

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 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

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

RMAT Approximate Power-Law Graph

Strongly Connected Components