Igraph’ Documentation of August 16, 2008

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Package ‘igraph’ documentation of August 16, 2008 Version 0.5.1 Date Feb 14, 2008 Title Routines for simple graphs, network analysis. Author Gabor Csardi <[email protected]> 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 Suggests stats4, rgl, tcltk, RSQLite, digest, graph, Matrix License GPL (>= 2) URL http://cneurocvs.rmki.kfki.hu/igraph R topics documented: igraph-package . .4 aging.prefatt.game . .5 alpha.centrality . .7 arpack . .9 articulation.points . 13 as.directed . 14 attributes . 15 barabasi.game . 17 betweenness . 19 biconnected.components . 21 bonpow . 22 canonical.permutation . 24 1 2 R topics documented: cliques . 26 closeness . 27 clusters . 29 cocitation . 30 cohesive.blocks . 31 edge.betweenness.community . 33 communities . 35 components . 36 constraint . 37 conversion . 38 decompose.graph . 39 degree . 40 degree.sequence.game . 41 diameter . 43 dyad.census . 44 edge.connectivity . 45 erdos.renyi.game . 46 evcent . 47 revolver ........................................... 49 fastgreedy.community . 53 forest.fire.game . 54 get.adjlist . 56 girth . 57 graph.adjacency . 58 Graphs from adjacency lists . 61 graph.automorphisms . 62 graph.constructors . 64 graph.data.frame . 66 graph.de.bruijn . 68 graph.density . 69 graph.famous . 70 graph.formula . 72 graph.graphdb . 74 graph-isomorphism . 76 graph.kautz . 79 graph.coreness . 80 graph.laplacian . 81 graph.lcf . 82 graph.maxflow . 83 graph-motifs . 85 igraph from/to graphNEL conversion . 86 graph.structure . 87 grg.game . 88 growing.random.game . 89 igraph-parameters . 90 igraph.sample . 91 Vertex shapes . 92 independent.vertex.sets . 93 R topics documented: 3 is.igraph . 95 is.multiple . 95 is.mutual . 97 iterators . 98 kleinberg . 100 layout.drl . 102 layout.merge . 104 layout . 105 leading.eigenvector.community . 109 line.graph . 112 measure.dynamics . 113 minimum.spanning.tree . 114 modularity . 116 neighborhood . 117 graph-operators . 118 page.rank . 120 permute.vertices . 122 plot.bgraph . 123 Drawing graphs . 124 plot.igraph . 130 power.law.fit . 131 preference.game . 132 print.igraph . 133 read.graph . 134 reciprocity . ..

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Planar Hypohamiltonian Graphs on 40 Vertices
Planar Hypohamiltonian Graphs on 40 Vertices Mohammadreza Jooyandeh, Brendan D. McKay Research School of Computer Science, Australian National University, ACT 2601, Australia Patric R. J. Osterg˚ard,¨ Ville H. Pettersson Department of Communications and Networking, Aalto University School of Electrical Engineering, P.O. Box 13000, 00076 Aalto, Finland Carol T. Zamfirescu Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 - S9, 9000 Ghent, Belgium Abstract A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 42 vertices, a result due to Araya and Wiener. That result is here improved upon by 25 planar hypohamiltonian graphs of order 40, which are found through computer-aided generation of certain families of planar graphs with girth 4 and a fixed number of 4-faces. It is further shown that planar hypohamiltonian graphs exist for all orders greater than or equal to 42. If Hamiltonian cycles are replaced by Hamilto- nian paths throughout the definition of hypohamiltonian graphs, we get the definition of hypotraceable graphs. It is shown that there is a planar hypo- traceable graph of order 154 and of all orders greater than or equal to 156. We also show that the smallest planar hypohamiltonian graph of girth 5 has 45 vertices. Email addresses: [email protected] (Mohammadreza Jooyandeh), [email protected] (Brendan D. McKay), [email protected] (Patric R. J. Osterg˚ard),¨ [email protected] (Ville H. Pettersson), [email protected] (Carol T. Zamfirescu) URL: http://www.jooyandeh.com (Mohammadreza Jooyandeh), http://cs.anu.edu.au/~bdm (Brendan D.
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Every Graph Occurs As an Induced Subgraph of Some Hypohamiltonian Graph
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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 .
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