The document provides an overview of graph theory and graph databases, detailing definitions, applications, and performance metrics. It discusses various types of graphs, their uses in fields such as logistics and network analysis, and highlights several graph database vendors. Additionally, it addresses performance comparisons and key features of different graph database systems.

1. Graph ( Theory and Databases )
Pere Urbón Bayes
Senior Software Engineer
Independent
purbon@purbon.com
purbon.com
in/purbon
December of 2010
@purbon

2. Graph (Theory and Databases)
● Graph Theory ● Graph Databases
– Definitions – Definitions
– Applications – Facts
– Analytics
– Performance
– Vendors
Graph ( Theory and Databases ) 2

3. Graph
Definitions
● Graph G(V,E) where V = {v1,v2,...,vN) and E =
{E1,E2,...,EN)
– Directed / Undirected
– Mixed
– Multigraph
– Weighted
– ....
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4. Graph
Definitions
● Directed graphs
● Vertex
● Edges
● From V(N) to V(M)
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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.
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6. Graph Theory
Applications
● Task planning
● Scheduling
● Process assignation
● Routing
● Logistics
● League planning
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7. Graph Theory
Applications
● Pattern Recognition
● Dependency analysis
● Impact analysis
● Network flow
– Traffic analysis and optimization
– Delivery optimization
● Optimization of tasks
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8. Graph Theory
analytics
● Clustering (Communities)
● Social connexions
● Hubs
● Graph Mining
● Centrality measures
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9. Graph Like
Applications
● Recommendations
– Heuristics (PageRank)
– Local
● Shortest Paths
● Hammock Functions
● Walks
● Search algorithms
● Shooting stars
● K-nearest neighbours
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10. Graph Like
Applications
● Location based services
● Hubs
● Spatial databases
● Logical (multi-)index construction
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11. Web
Trending Topics
● Semantic web
– RDF (OWL) Store
– RDF-Sail
– SPARQL
● Linked data (Open Data)
● Link analysis
● Structure mining
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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
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13. Graph databases
Property graph
● Abstractions
– Nodes
– Relationships
– Properties on both.
John smith liked http://www.example.com at 01/10/11
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14. Graph databases
Facts
Connectivity
Everything
connected
RDF Ontologies
Linked Data
Tagging
Blogs Folksonomies
Social Networks
Text files
1990's 2010's 2020's Decades
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15. Graph databases
Facts
Size of
1990's 2010's 2020's Decades
Graph ( Theory and Databases ) 15
http://www.guardian.co.uk/business/2009/may/18/digital-content-expansion

16. Graph databases
Facts
Performance
Lists
Graph like structures
Semantic web
Semantic reasoning
Linked data
Performance slowdown
Unstructured
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17. Graph databases
Performance
Kernel DEX Neo4j Jena HyperGraphDB
Scale 15
Load(s) 7,44 697 141 +24h
Scan (s) 0,0010 2,71 0,689
2-Hops(s) 0,0120 0,0260 0,443
BC (s) 14,8 8,24 138
Size (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 ) 17
HPC Scalable Graph Analysis Benchmark IWGD 2010

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.
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19. Graph ( Theory and Databases )
Thanks!
purbon@purbon.com
December of 2010
Graph ( Theory and Databases ) 19