The document provides an overview of graphs and databases, outlining definitions, use cases, and examples of different types of graphs, including directed and undirected graphs. It discusses how to store graphs and perform queries using ArangoDB, highlighting the mechanisms for traversing and visualizing graph data. Additionally, it includes practical demonstrations on creating databases, adding edges, and executing traversals.

1. Graphs, Databases and what we can use them for
Michael Hackstein
@mchacki
November 6, 2013
c 2013 triAGENS GmbH | 2013-11-6

2. About me
Still Student (Master Informatik) at RWTH
Just handed in my thesis
Software developer at triAGENS GmbH, CGN
Part of the ArangoDB team
c 2013 triAGENS GmbH | 2013-11-6

3. Table of contents
1 Definition
2 Use Cases
3 Databases
4 Traversals
5 Visualisation
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4. What is a graph?
A set of arbitrary objects, called vertices
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5. What is a graph?
A set of arbitrary objects, called vertices
And a set of relations between them, called edges
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6. Formal Definition
Let V be the set of vertices
Let E ⊆ V × V be the set of edges
Define G = (V , E ) is a graph
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7. Formal Definition
Let V be the set of vertices
Let E ⊆ V × V be the set of edges
Define G = (V , E ) is a graph
Define δ + (n) =
v ∈V |(n,v )∈E
1 is the indegree of n ∈ V
Define δ − (n) =
1 is the outdegree of n ∈ V
Define δ(n) =
as the degree of n ∈ V
v ∈V |(v ,n)∈E
δ + (n) + δ − (n)
c 2013 triAGENS GmbH | 2013-11-6

8. Directed Graphs
Edges have a direction
One vertex is the source
The other vertex is the target
Formal: (a, b) ∈ E
(b, a) ∈ E
And (a, b) ∈ E ∧ (b, a) ∈ E ⇒ (a, b) = (b, a)
c
d
b
a
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9. Example: Navigation Systems
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10. Undirected Graphs
Edges do not have a direction
No vertex is source or target
Formal: (a, b) ∈ E ⇔ (b, a) ∈ E
And (a, b) ∈ E ∧ (b, a) ∈ E ⇒ (a, b) = (b, a)
c
d
b
a
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11. Example: Social Networks
Charly
Diana
Bob
Alice
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12. Property Graphs
Vertices have properties in addition to a label
Edges have properties in addition to a label
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13. Graphs in Relational Databases
m
Edge
Vertex
n
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14. Where else to store Graphs?
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15. How to store Graphs?
We will have an example using ArangoDB.
First Example: Create new database using Graphs API
DEMO TIME
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16. How to store Graphs?
Second Example: You already have vertices.
How to add edges?
DEMO TIME
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17. But what can we do with the data now?
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18. Queries on graphs
Mechanism to query a graph
Starts at one specific vertex
Searches all connected vertices
Searches children of these vertices
Until predefined boundary is reached
Order of vertices can be configured
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19. The visitor
Active at each searched vertex
Can execute queries on this vertex like collecting attributes
Does know the path followed to reach the current vertex
Does not know vertices that will be visited in future
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20. Traversals
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21. Traversals
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22. Traversals
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23. Traversals
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24. Traversals
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25. Traversals
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26. Traversals
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27. Traversals
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28. Traversals
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31. Traversals
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32. Traversals
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37. Traversals
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38. Traversals Live
Example: Execute traversal in ArangoDB
DEMO TIME
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39. Visualisation
Example: How to view the graph
DEMO TIME
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