Graphs, Databases and what we can use them for

Michael Hackstein@mchacki

November 6, 2013

c©2013 triAGENS GmbH | 2013-11-6

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

Table of contents

1 Definition

2 Use Cases

3 Databases

4 Traversals

5 Visualisation

c©2013 triAGENS GmbH | 2013-11-6

What is a graph?

A set of arbitrary objects, called vertices

And a set of relations between them, called edges

c©2013 triAGENS GmbH | 2013-11-6

What is a graph?

A set of arbitrary objects, called verticesAnd a set of relations between them, called edges

c©2013 triAGENS GmbH | 2013-11-6

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

c©2013 triAGENS GmbH | 2013-11-6

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

Define δ+(n) =∑

v∈V |(n,v)∈E 1 is the indegree of n ∈ V

Define δ−(n) =∑

v∈V |(v ,n)∈E 1 is the outdegree of n ∈ V

Define δ(n) = δ+(n) + δ−(n) as the degree of n ∈ V

c©2013 triAGENS GmbH | 2013-11-6

Directed Graphs

Edges have a directionOne vertex is the sourceThe other vertex is the targetFormal: (a, b) ∈ E ; (b, a) ∈ EAnd (a, b) ∈ E ∧ (b, a) ∈ E ⇒ (a, b) 6= (b, a)

a

b

c

d

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Example: Navigation Systems

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Undirected Graphs

Edges do not have a directionNo vertex is source or targetFormal: (a, b) ∈ E ⇔ (b, a) ∈ EAnd (a, b) ∈ E ∧ (b, a) ∈ E ⇒ (a, b) = (b, a)

a

b

c

d

c©2013 triAGENS GmbH | 2013-11-6

Example: Social Networks

Alice

Bob

Charly

Diana

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Property Graphs

Vertices have properties in addition to a labelEdges have properties in addition to a label

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Graphs in Relational Databases

Vertex Edge

m

n

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Where else to store Graphs?

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How to store Graphs?

We will have an example using ArangoDB.

First Example: Create new database using Graphs API

DEMO TIME

c©2013 triAGENS GmbH | 2013-11-6

How to store Graphs?

Second Example: You already have vertices.

How to add edges?

DEMO TIME

c©2013 triAGENS GmbH | 2013-11-6

But what can we do with the data now?

c©2013 triAGENS GmbH | 2013-11-6

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

c©2013 triAGENS GmbH | 2013-11-6

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

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

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Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

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Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 0 Nuts: 0

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

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Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 0 Nuts: 0

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 0 Nuts: 0

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 2 Nuts: 3

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Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 2 Nuts: 3

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 2 Nuts: 3

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 4 Nuts: 3

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 4 Nuts: 3

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 4 Nuts: 3

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 9 Nuts: 8

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 9 Nuts: 8

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 9 Nuts: 8

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 10 Nuts: 9

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 12 Nuts: 10

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 12 Nuts: 12

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 13 Nuts: 13

c©2013 triAGENS GmbH | 2013-11-6

Traversals

Grain: 0Nuts: 0

Grain: 2Nuts: 3

Grain: 1Nuts: 1

Grain: 0Nuts: 2

Grain: 2Nuts: 0

Grain: 5Nuts: 5

Grain: 2Nuts: 1

Grain: 1Nuts: 1

Grain: 8Nuts: 9

Grain: 13 Nuts: 13 Done

c©2013 triAGENS GmbH | 2013-11-6

Traversals Live

Example: Execute traversal in ArangoDB

DEMO TIME

c©2013 triAGENS GmbH | 2013-11-6

Visualisation

Example: How to view the graph

DEMO TIME

c©2013 triAGENS GmbH | 2013-11-6