An Introduction to Graph Databases

www.Objectivity.com

An Introduction To
Graph Databases
Leon Guzenda & Nick Quinn
August 20, 2013

Overview
• Introductions
• Graph Theory
• Commonly Used Graph Algorithms
• Graph Databases
• Current Implementations
• Use Cases
• Hands-On Tutorial

We Are From Objectivity Inc.
Company

• Objectivity, Inc. is headquartered in Sunnyvale, CA.
• Established in 1988 to tackle database problems that network/hierarchical/relational and file-based technologies
struggle with.
• Objectivity has over two decades of Big Data and NoSQL experience

Products

• Develops NoSQL platforms for managing and discovering relationships and patterns in complex data:
• Objectivity/DB - an object database that manages localized, centralized or distributed databases
• InfiniteGraph

- a massively scalable graph database built on Objectivity/DB that enables

organizations to find, store and exploit the relationships in their data

Markets

• The Big Data market is projected to be around $12B in 2012, with a CAGR of 28% over the next five years.
• 40% per year data growth, cloud adoption, mobile usage and improved real-time analytics underpin Objectivity’s
growth opportunities as a Big Data analytics enabler.

Customers

• Embedded in hundreds of enterprises, government organizations and products - millions of deployments.

Financials

• Consistently generates increased revenues.
• Privately held by the employees and a few venture capital companies.

Copyright © Objectivity, Inc. 2012

The History of Graph Theory
1736: Leonard Euler writes a paper on the “Seven Bridges of Konisberg”
1845: Gustav Kirchoff publishes his electrical circuit laws
1852: Francis Guthrie poses the “Four Color Problem”
1878: Sylvester publishes an article in Nature magazine that describes graphs
1936: Dénes Kőnig publishes a textbook on Graph Theory
1941: Ramsey and Turán define Extremal Graph Theory
1959: De Bruijn publishes a paper summarizing Enumerative Graph Theory
1959: Erdos, Renyi and Gilbert define Random Graph Theory
1969: Heinrich Heesch solves the “Four Color” problem
2003: Commercial Graph Database products start appearing on the market

Graph Theory Terminology...
VERTEX: A single node in a graph data structure
EDGE: A connection between a pair of VERTICES
PROPERTIES: Data items that belong to a particular Vertex or Edge
WEIGHT: A quantity associated with a particular Edge
GRAPH: A network of linked Vertex and Edge objects

Vertex 1
City: San Francisco
Pop: 812,826

Edge 1
Road: I-101
Miles: 47.8

Vertex 2
City: San Jose
Pop: 967,487

...Graph Theory Terminology...
SIMPLE/UNDIRECTED GRAPH: A Graph where each VERTEX may be linked to

one or more Vertex objects via Edge objects and each Edge object is connected to
exactly two Vertex objects. Furthermore, neither Vertex connected to an Edge is more
significant than the other.

DIRECTED GRAPH: A Simple/Undirected Graph where one Vertex in a

Vertex + Edge + Vertex group (an “Arc” or “Path”) can be considered the “Head” of the
Path and the other can be considered the “Tail”.

MIXED GRAPH: A Graph in which some paths are Undirected and others are
Directed.

...Graph Theory Terminology
LOOP: An Edge that is doubly-linked to the same Vertex
MULTIGRAPH: A Graph that allows multiple Edges and Loops
QUIVER: A Graph where Vertices are allowed to be connected by multiple Arcs.
A Quiver may include Loops.

WEIGHTED GRAPH: A Graph where a quantity is assigned to an Edge, e.g.

a Length assigned to an Edge representing a road between two Vertices representing
cities.

 HALF EDGE: An Edge that is only connected to a single Vertex
 LOOSE EDGE: An Edge that isn't connected to any Vertices.
 CONNECTIVITY: Two Vertices are Connected if it is possible to find a path between
them.

COMMONLY USED GRAPH ALGORITHMS

Mac Evans

Commonly Used Graph Algorithms...
CONNECTEDNESS: Check whether or not a set of nodes in a Graph are connected.
All of the nodes in the graph below are connected, e.g. A to B, A to C via B etc.

SHORTEST PATH: The path between two nodes that visits the fewest intermediate nodes.
In the graph above, A->B->C->D is shorter than A->B->C->B->D (disallowing loops)

NODE DEGREE: The degree of a node in a network is a count of the number of

connections it has to other nodes. The degree distribution is the probability distribution of
these degrees in the whole network.
In the graph below, A and D have a node degree of 1. B and C have a node degree of 3.

...Commonly Used Graph Algorithms...
CENTRALITY: An assessment of the importance of a node within a network.
Degree Centrality is the simplest, being a count of the number of connections that a node has.
It may be expressed as “Indegree” (# of incoming connections) and “Outdegre” (# of outgoing
connections).

CLOSENESS CENTRALITY: Closeness considers the shortest paths between nodes and
assigns a higher value to nodes that can be used to reach most other nodes most quickly.

In the graph below, node A has the greatest centrality as all other nodes can be reached in one
“hop”, whereas others require 1 hop to A or 2 hops to any other node.

A

Commonly Used Graph Algorithms...
CONNECTEDNESS: Check whether or not a set of nodes in a Graph are connected.
All of the nodes in the graph below are connected, e.g. A to B, A to C via B etc.

In the graph above, A->B->C->D is shorter than A->B->C->B->D (disallowing loops)

NODE DEGREE: The degree of a node in a network is a count of the number of

connections it has to other nodes. The degree distribution is the probability distribution of
these degrees in the whole network.
In the graph below, A and D have a node degree of 1. B andC have a node degree of 3.

In the graph below, A->B->C->D is shorter than A->B->C->B->D (disallowing loops)

AVERAGE PATH LENGTH: The average of all path lengths between all pairs of nodes in a
graph.

TRANSITIVE CLOSURE: The process of exploring a graph by traversing relationships
until all nodes have been visited, but without revisiting nodes that are joined together in
loops.
In the graph above, A->B->C->D is a transitive closure.

GRAPH DIAMETER (or SPAN): The greatest distance between any pair of nodes in a graph.
It is computed by finding the shortest path between each pair of nodes. The maximum of these
path lengths is a measure of the diameter of the graph.
The diameters of the two graphs below are 2 and 5.

BETWEENESS CENTRALITY: A centrality measure of a node within a graph.
Nodes that have a high probability of being visited on a randomly chosen short path between two
randomly chosen nodes have a high “betweeness”
In the graph below, node D has the highest betweeness centrality.

Recognizing Graphs In Object Models...
Tree Structures
1-to-Many

Object Class A

...Recognizing Graphs In Object Models...
Tree Structures
1-to-Many

Relationship
Data

Object Class A

Object Class A

Tree Structures
1-to-Many

Relationship
Data

Object Class A

Object Class A

Graph (Network) Structures
Many-to-Many

Object Class A

Tree Structures
1-to-Many

Relationship
Data

Object Class A

Object Class A

Many-to-Many

Relationship Data

Object Class A

Object Class A


Why Do We Need Graph DBMSs?...
Relational Database
Think about the SQL query for finding all links between the two “blue” rows... Good luck!
Table_A

Table_B

Table_C

Table_D

Table_E

Table_F

Table_G

Relational databases aren’t good at handling complex relationships!

...Graph DBMSs Are Designed To Handle Relationships
Relational Database
Think about the SQL query for finding all links between the two “blue” rows... Good luck!
Table_A

Table_B

Table_C

Table_D

Table_E

Table_F

Table_G

Objectivity/DB or InfiniteGraph - The solution can be found with a few lines of code
A3

G4

Graph Databases
• Data model:
– Node (Vertex) and Relationship (Edge) objects
– Directed
– May be a hypergraph (edges with multiple endpoints)

• Examples:
– InfiniteGraph, Neo4j, OrientDB, AllegroGraph, TitanDB and Dex

VERTEX

2

N

EDGE

Graph DBMSs Use A Very Simple Object Model
Tree Structures
1-to-Many

Relationship
Data

Object Class A

Object Class A


GRAPH MODEL

Many-to-Many

Relationship Data

EDGE

Object Class A

Object Class A

VERTEX


Basic Capabilities Of Most Graph Databases...
Rapid Graph Traversal

Start

Finish

...Basic Capabilities Of Most Graph Databases...

Inclusive or Exclusive Selection

X
Start

Start

X

...Basic Capabilities Of Most Graph Databases


X
Start

Start

X
Find the Shortest or All Paths Between Objects

Start

Finish

InfiniteGraph Capabilities
Parallel Graph Traversal


X
Start

Start

X
Shortest or All Paths Between Objects

Computational & Visualization Plug-Ins
Compute Cost To Date

Start

Finish

Start

Visualize


Graph Databases Post-2003

X
Titan

Graph Databases Compared [UNSW]
DATA STORAGE FEATURES

Graph Databases Compared [DZone]

Source: http://goo.gl/ni4eoE

Graph Databases – Pros and Cons
• Strengths:
– Extremely fast for connected data
– Scales out, typically
– Easy to query (navigation)
– Simple data model

• Weaknesses:
– May not support distribution or sharding
– Requires conceptual shift... a different way of thinking

VERTEX

2

N

EDGE

Example 1 - Market Analysis
The 10 companies that control a majority of U.S. consumer goods brands

Example 2 - Demographics
Used in social network analysis, marketing, medical research etc.

Example 3 - Seed To Consumer Tracking

?

Example 4 - Ad Placement Networks
Smartphone Ad placement - based on the the user’s profile and location data
captured by opt-in applications.
• The location data can be stored and distilled in a key-value and column store
hybrid database, such as Cassandra
• The locations are matched with geospatial data to deduce user interests.
• As Ad placement orders arrive, an application built on a graph database such
as InfiniteGraph, matches groups of users with Ads:
• Maximizes relevance for the user.
• Yields maximum value for the advertiser and the placer.

Example 5 - Healthcare Informatics

Problem: Physicians need better electronic records for managing patient data on a global
basis and match symptoms, causes, treatments and interdependencies to improve
diagnoses and outcomes.
• Solution: Create a database capable of leveraging existing architecture using NOSQL tools
such as Objectivity/DB and InfiniteGraph that can handle data capture, symptoms,
diagnoses, treatments, reactions to medications, interactions and progress.
• Result: It works:
• Diagnosis is faster and more accurate
• The knowledge base tracks similar medical cases.
• Treatment success rates have improved.

Example 6 - Big Data Analytics

Example 7 – Visual Analytics

Hands On With A Graph Database

• We'll be using InfiniteGraph today
• You'll need a Java Development environment on your machine

• If you haven't downloaded InfiniteGraph already, please go to:
http://goo.gl/XzJo6T [https://download.infinitegraph.com/index.aspx]

• We'll be covering a HelloGraph and a more complex sample program

An Introduction to Graph Databases

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