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# Graph Theory and Databases

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This presentation is an overview of some applications of graph theory that graphdbs has bring into reality.

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### Graph Theory and Databases

1. 1. Graph ( Theory and Databases ) Pere Urbón Bayes Senior Software Engineer Independent purbon@purbon.com purbon.com in/purbon December of 2010 @purbon
2. 2. Graph (Theory and Databases)● Graph Theory ● Graph Databases – Definitions – Definitions – Applications – Facts – Analytics – Performance – Vendors Graph ( Theory and Databases ) 2
3. 3. Graph Definitions● Graph G(V,E) where V = {v1,v2,...,vN) and E = {E1,E2,...,EN) – Directed / Undirected – Mixed – Multigraph – Weighted – .... Graph ( Theory and Databases ) 3
4. 4. Graph Definitions● Directed graphs● Vertex● Edges● From V(N) to V(M) Graph ( Theory and Databases ) 4
5. 5. Graph Definitions Multigraph Labelling● More than one edge ● The process of between two nodes. assigning a label to a● Loops, edges vertex and edges. between the same node. Graph ( Theory and Databases ) 5
6. 6. Graph Theory Applications● Task planning● Scheduling● Process assignation● Routing● Logistics● League planning Graph ( Theory and Databases ) 6
7. 7. Graph Theory Applications● Pattern Recognition● Dependency analysis● Impact analysis● Network flow – Traffic analysis and optimization – Delivery optimization● Optimization of tasks Graph ( Theory and Databases ) 7
8. 8. Graph Theory analytics● Clustering (Communities)● Social connexions● Hubs● Graph Mining● Centrality measures Graph ( Theory and Databases ) 8
9. 9. Graph Like Applications● Recommendations – Heuristics (PageRank) – Local ● Shortest Paths ● Hammock Functions ● Walks ● Search algorithms ● Shooting stars ● K-nearest neighbours Graph ( Theory and Databases ) 9
10. 10. Graph Like Applications● Location based services● Hubs● Spatial databases● Logical (multi-)index construction Graph ( Theory and Databases ) 10
11. 11. Web Trending Topics● Semantic web – RDF (OWL) Store – RDF-Sail – SPARQL● Linked data (Open Data)● Link analysis● Structure mining Graph ( Theory and Databases ) 11
12. 12. Graph databases“A graph database is a database that uses graph structures with nodes, edges, and properties to represent and store information. General graph databases that can store any graph are distinct from specialized graph databases such as triple stores and network databases.” Wikipedia Graph ( Theory and Databases ) 12
13. 13. Graph databases Property graph● Abstractions – Nodes – Relationships – Properties on both. John smith liked http://www.example.com at 01/10/11 Graph ( Theory and Databases ) 13
14. 14. Graph databases FactsConnectivity Everything connected RDF Ontologies Linked Data Tagging Blogs Folksonomies Social Networks Text files 1990s 2010s 2020s Decades Graph ( Theory and Databases ) 14
15. 15. Graph databases FactsSize of 1990s 2010s 2020s Decades Graph ( Theory and Databases ) 15 http://www.guardian.co.uk/business/2009/may/18/digital-content-expansion
16. 16. Graph databases FactsPerformance Lists Graph like structures Semantic web Semantic reasoning Linked data Performance slowdown Unstructured Graph ( Theory and Databases ) 16
17. 17. Graph databases PerformanceKernel DEX Neo4j Jena HyperGraphDBScale 15Load(s) 7,44 697 141 +24hScan (s) 0,0010 2,71 0,6892-Hops(s) 0,0120 0,0260 0,443BC (s) 14,8 8,24 138Size (MB) 30 17 207 Kernel DEX Neo4j Jena HyperGraph Scale 20 DB Load(s) 317 32.094 4.560 +24h Scan (s) 0,005 751 18,6 2-Hops(s) 0,033 0,0230 0,4580 BC (s) 617 7027 59512 Size (MB) 893 539 6656 Graph ( Theory and Databases ) 17HPC Scalable Graph Analysis Benchmark IWGD 2010
18. 18. Graph databases Vendors● Neo4J: Open source database NoSQL graph.● Dex: The high performance graph database.● HyperGraphDB: An IA and semantic web graph database.● Infogrid: The Internet Graph database.● Sones: SaaS dot Net Graph database.● VertexDB: High performance database server. Graph ( Theory and Databases ) 18
19. 19. Graph ( Theory and Databases ) Thanks! purbon@purbon.com December of 2010 Graph ( Theory and Databases ) 19