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Package ‘igraph’ February 28, 2013 Version 0.6.5-1 Date 2013-02-27 Title Network analysis and visualization Author See AUTHORS file. Maintainer Gabor Csardi <[email protected]> Description Routines for simple graphs and network analysis. igraph can handle large graphs very well and provides functions for generating random and regular graphs, graph visualization,centrality indices and much more. Depends stats Imports Matrix Suggests igraphdata, stats4, rgl, tcltk, graph, Matrix, ape, XML,jpeg, png License GPL (>= 2) URL http://igraph.sourceforge.net SystemRequirements gmp, libxml2 NeedsCompilation yes Repository CRAN Date/Publication 2013-02-28 07:57:40 R topics documented: igraph-package . .5 aging.prefatt.game . .8 alpha.centrality . 10 arpack . 11 articulation.points . 15 as.directed . 16 1 2 R topics documented: as.igraph . 18 assortativity . 19 attributes . 21 autocurve.edges . 23 barabasi.game . 24 betweenness . 26 biconnected.components . 28 bipartite.mapping . 29 bipartite.projection . 31 bonpow . 32 canonical.permutation . 34 centralization . 36 cliques . 39 closeness . 40 clusters . 42 cocitation . 43 cohesive.blocks . 44 Combining attributes . 48 communities . 51 community.to.membership . 55 compare.communities . 56 components . 57 constraint . 58 contract.vertices . 59 conversion . 60 conversion between igraph and graphNEL graphs . 62 convex.hull . 63 decompose.graph . 64 degree . 65 degree.sequence.game . 66 dendPlot . 67 dendPlot.communities . 68 dendPlot.igraphHRG . 70 diameter . 72 dominator.tree . 73 Drawing graphs . 74 dyad.census . 80 eccentricity . 81 edge.betweenness.community . 82 edge.connectivity . 84 erdos.renyi.game . 86 evcent . 87 fastgreedy.community . 89 forest.fire.game . 90 get.adjlist . 92 get.edge.ids . 93 get.incidence . 94 get.stochastic . 95 R topics documented: 3 girth . 96 graph-isomorphism . 97 graph-motifs . 101 graph-operators . 103 graph-operators-by-name . 104 graph.adjacency . 106 graph.automorphisms . 109 graph.bfs . 110 graph.bipartite . 112 graph.constructors . 114 graph.coreness . 116 graph.data.frame . 117 graph.de.bruijn . 119 graph.density . 120 graph.dfs . 121 graph.diversity . 123 graph.famous . 125 graph.formula . 127 graph.full.bipartite . 129 graph.graphdb . 130 graph.incidence . 132 graph.kautz . 133 graph.knn . 134 graph.laplacian . 136 graph.lcf . 137 graph.matching . 138 graph.maxflow . 140 graph.strength . 142 graph.structure . 143 Graphs from adjacency lists . 150 grg.game . ..

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Practical Parallel Hypergraph Algorithms
Practical Parallel Hypergraph Algorithms Julian Shun [email protected] MIT CSAIL Abstract v While there has been signicant work on parallel graph pro- 0 cessing, there has been very surprisingly little work on high- e0 performance hypergraph processing. This paper presents v0 v1 v1 a collection of ecient parallel algorithms for hypergraph processing, including algorithms for betweenness central- e1 ity, maximal independent set, k-core decomposition, hyper- v2 trees, hyperpaths, connected components, PageRank, and v2 v3 e single-source shortest paths. For these problems, we either 2 provide new parallel algorithms or more ecient implemen- v3 tations than prior work. Furthermore, our algorithms are theoretically-ecient in terms of work and depth. To imple- (a) Hypergraph (b) Bipartite representation ment our algorithms, we extend the Ligra graph processing Figure 1. An example hypergraph representing the groups framework to support hypergraphs, and our implementa- , , , , , , and , , and its bipartite repre- { 0 1 2} { 1 2 3} { 0 3} tions benet from graph optimizations including switching sentation. between sparse and dense traversals based on the frontier size, edge-aware parallelization, using buckets to prioritize processing of vertices, and compression. Our experiments represented as hyperedges, can contain an arbitrary number on a 72-core machine and show that our algorithms obtain of vertices. Hyperedges correspond to group relationships excellent parallel speedups, and are signicantly faster than among vertices (e.g., a community in a social network). An algorithms in existing hypergraph processing frameworks. example of a hypergraph is shown in Figure 1a. CCS Concepts • Computing methodologies → Paral- Hypergraphs have been shown to enable richer analy- lel algorithms; Shared memory algorithms.
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Q(A) - Balance Super Edge Magic Graphs Results
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Practical Parallel Hypergraph Algorithms
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Adjacency Matrix
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