PPT-9.3 Representing Graphs and Graph Isomorphism

Sometimes two graphs have exactly the same form in the sense that there is a onetoone correspondence between their vertex sets that preserves edges In such a case we say that the two graphs are . Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,. Dr. Andrew Wallace PhD . BEng. (hons) . EurIng. andrew.wallace@cs.umu.se. Overview. Sets. Implementation. Complexity. Graphs. Constructing . Graphs. Graph examples. Sets. Collection of items. No specified ordered. Nodes. Blank nodes are great!. Blank Nodes are Great!. Blank Nodes are Glue!. Blank Nodes names aren’t important …. (Isomorphic). BUT Blank nodes. ADD COMPLEXITY…. Are two RDF graphs isomorphic?. Isabelle Stanton, UC Berkeley. Gabriel . Kliot. , Microsoft Research XCG. Modern graph datasets are huge. The web graph had over a trillion links in 2011. Now?. . facebook. has “more than 901 million users with average degree 130”. Arijit Khan, . Yinghui. Wu, Xifeng Yan. Department of Computer Science. University of California, Santa Barbara. {. arijitkhan. , . yinghui. , . xyan. }@. cs.ucsb.edu. Graph Data. 2. Graphs are everywhere.. Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,. infinite random geometric . g. raphs. Anthony Bonato. Ryerson University. Random Geometric Graphs . and . Their Applications to Complex . Networks. BIRS. R. Infinite random geometric graphs. 111. 110. Section . 10.3. Representing Graphs: . Adjacency Lists. Definition. : An . adjacency list . can be used to represent a graph with no multiple edges by specifying the vertices that are adjacent to each vertex of the graph.. The type of graph you draw depends on the types of observations you make. Bar Graph. Line Graph. Pie Graph. Bar and Column Graphs. Bar and column graphs. Some observations fall into . discrete. groupings. Distance/Time. Distance. Distance. Distance. D. t. D. t. D. t. Gradient = . speed. Distance-Time graph. gradient = velocity. Graphs Representing Motion. Velocity-time graph. Gradient = acceleration. Area . Graph Isomorphism. 2. Today. Graph isomorphism: definition. Complexity: isomorphism completeness. The refinement heuristic. Isomorphism for trees. Rooted trees. Unrooted trees. Graph Isomorphism. 3. Graph Isomorphism. (and related problems). on Minor-Free Graphs. Hans . Bodlaender. (U Utrecht, TU Eindhoven). Jesper. . Nederlof. (TU Eindhoven). Tom van der . Zanden. (U Utrecht). 1. Subgraph Isomorphism. Given: a . Lasserre. Gaps,. and Asymmetry of Random Graphs. Ryan O’Donnell (CMU). John Wright (CMU). Chenggang. Wu (. Tsinghua. ). Yuan Zhou (CMU). Hardness of . Robust Graph Isomorphism. ,. . Lasserre. Gaps,.