Graph Algorithms and Databases

1. GraphAlgorithms and Databases DušanZeleník

2. Common Tasks • Sorting • Searching • Inferring • Routing

3. Entities and their properties • Single attribute entities • Simple ordinal values • Relatively easy to sort or search • Low complexity • Indexing • Multi attribute entities • Relations among entities • Calculating distances (similarity) • Discovering properties

4. Trees and Graphs • Tree is a graph • Balancing • Lowering the complexity ( O(log n) ) • Graph • Triplets (S - P - O) • Complex structure with properties • Polynomial compelxity ( O(n^k) )

5. Spreading Activation • Select initial nodes and fill them with energy • Spread energy from nodes • Split energy among associated nodes • Mark nodes as already used • Do not spread if energy is under threshold • Repeat spreading until convergence

6. Page Rank • Each node receives initial rank • Count outgoing edges C(node) • Page Rank for Node A is PR(A) = =(1- d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn)) PR(A) is the PageRank of page A, PR(Ti) is the PageRankof pages Ti which link to page A, C(Ti) is the number of outbound links on page Ti d is a damping factor which can be set between 0 and 1.

7. Neo4J Database • Java • SPARQL, cypher, gremlin • ACID • Multiplatform • Opensource • Plugins • Already implements many algorithms • REST

8. Neo4J Hello World Node f = graphDb.createNode(); f.setProperty("message","Hello"); Node s = graphDb.createNode(); s.setProperty("message","World!"); Relationship r = f.createRelationshipTo(s, RelTypes.KNOWS ); r.delete(); f.delete(); s.delete();

9. Neo4J Graph Algorithms PathFinder<WeightedPath> finder = GraphAlgoFactory.dijkstra( Traversal.expanderForTypes( ExampleTypes.MY_TYPE, Direction.BOTH ), "cost" ); WeightedPathpath = finder.findSinglePath( nodeA, nodeB ); path.weight();

10. Neo4J Plugin publicclassShortestPathextendsServerPlugin{     @Description( "Findtheshortestpathbetweentwonodes." )     @PluginTarget( Node.class ) publicIterable<Path> shortestPath(@SourceNodesource,                 @Parameter( name = "target" ) Nodetarget,                 @Parameter( name = "types", optional = true ) String[] types,                 @Parameter( name = "depth", optional = true ) Integerdepth ) { Expanderexpander; if ( types == null ) expander = Traversal.expanderForAllTypes(); else { expander = Traversal.emptyExpander(); for ( int i = 0; i < types.length; i++ ) expander = expander.add( DynamicRelationshipType.withName( types[i] ) );         } PathFinder<Path> shortestPath = GraphAlgoFactory.shortestPath( expander, depth == null ? 4 : depth.intValue() ); returnshortestPath.findAllPaths( source, target );     } } curl -X POST http://localhost:7474/db/data/ext/GetAll/node/123/shortestPath \   -H "Content-Type: application/json" \   -d '{"target":"http://localhost:7474/db/data/node/456&depth=5"}'

11. Research and Graphs • Z. Huang, W. Chung, T.-H. Ong, and H. Chen, “A graphbased recommender system for digital library,” in Proceedings of the 2nd ACM/IEEE-CS joint conference on Digital libraries, ser. JCDL ’02. New York, NY, USA: ACM, 2002,pp. 65–73. • I. Mele, F. Bonchi, and A. Gionis, “The early-adopter graph and its application to web-page recommendation.” New York, New York, USA: ACM Press, 2012, p. 1682. • S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, “Extrapolation methods for accelerating pagerank computations,” in Proceedings of the 12th international conference on World Wide Web, ser. WWW ’03. New York, NY, USA: ACM, 2003, pp. 261–270. • Y. Deng, Z. Wu, C. Tang, H. Si, H. Xiong, and Z. Chen, “A Hybrid Movie Recommender Based on Ontology and Neural Networks.” Ieee, Dec. 2010, pp. 846–851. • B. Chen, J. Wang, Q. Huang, and T. Mei, “Personalized video recommendation through tripartite graph propagation.” New York, New York, USA: ACM Press, 2012, p. 1133.