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The world is driven by connections—from financial and communication systems to
social and biological processes. Revealing the meaning behind these connections
drives breakthroughs across industries in areas such as identifying fraud rings and
optimizing recommendations to evaluating the strength of a group and predicting
cascading failures.
As connectedness continues to accelerate, it’s not surprising that interest in graph
algorithms has exploded because they are based on mathematics explicitly developed
to gain insights from the relationships between data. Graph analytics can uncover the
workings of intricate systems and networks at massive scales—for any organization.
We are passionate about the utility and importance of graph analytics as well as the
joy of uncovering the inner workings of complex scenarios. Until recently, adopting
graph analytics required significant expertise and determination, because tools and
integrations were difficult and few knew how to apply graph algorithms to their
quandaries. It is our goal to help change this. We wrote this book to help organiza‐
tions better leverage graph analytics so that they can make new discoveries and
develop intelligent solutions faster.
What’s in This Book
This book is a practical guide to getting started with graph algorithms for developers
and data scientists who have experience using Apache Spark™ or Neo4j. Although our
algorithm examples utilize the Spark and Neo4j platforms, this book will also be help‐
ful for understanding more general graph concepts, regardless of your choice of
graph technologies.
The first two chapters provide an introduction to graph analytics, algorithms, and
theory. The third chapter briefly covers the platforms used in this book before we
dive into three chapters focusing on classic graph algorithms: pathfinding, centrality,
and community detection. We wrap up the book with two chapters showing how
ix
graph algorithms are used within workflows: one for general analysis and one for
machine learning.
At the beginning of each category of algorithms, there is a reference table to help you
quickly jump to the relevant algorithm. For each algorithm, you’ll find:
• An explanation of what the algorithm does
• Use cases for the algorithm and references to where you can learn more
• Example code providing concrete ways to use the algorithm in Spark, Neo4j, or
both
Conventions Used in This Book
The following typographical conventions are used in this book:
Italic
Indicates new terms, URLs, email addresses, filenames, and file extensions.
Constant width
Used for program listings, as well as within paragraphs to refer to program ele‐
ments such as variable or function names, databases, data types, environment
variables, statements, and keywords.
Constant width bold
Shows commands or other text that should be typed literally by the user.
Constant width italic
Shows text that should be replaced with user-supplied values or by values deter‐
mined by context.
This element signifies a tip or suggestion.
This element signifies a general note.
x | Preface
This element indicates a warning or caution.
Using Code Examples
Supplemental material (code examples, exercises, etc.) is available for download at
https://bit.ly/2FPgGVV.
This book is here to help you get your job done. In general, if example code is offered
with this book, you may use it in your programs and documentation. You do not
need to contact us for permission unless you’re reproducing a significant portion of
the code. For example, writing a program that uses several chunks of code from this
book does not require permission. Selling or distributing a CD-ROM of examples
from O’Reilly books does require permission. Answering a question by citing this
book and quoting example code does not require permission. Incorporating a signifi‐
cant amount of example code from this book into your product’s documentation does
require permission.
We appreciate, but do not require, attribution. An attribution usually includes the
title, author, publisher, and ISBN. For example: “Graph Algorithms by Amy E. Hodler
and Mark Needham (O’Reilly). Copyright 2019 Amy E. Hodler and Mark Needham,
978-1-492-05781-9.”
If you feel your use of code examples falls outside fair use or the permission given
above, feel free to contact us at permissions@oreilly.com.
O’Reilly Online Learning
For almost 40 years, O’Reilly has provided technology and
business training, knowledge, and insight to help companies
succeed.
Our unique network of experts and innovators share their knowledge and expertise
through books, articles, and our online learning platform. O’Reilly’s online learning
platform gives you on-demand access to live training courses, in-depth learning
paths, interactive coding environments, and a vast collection of text and video from
O’Reilly and 200+ other publishers. For more information, please visit http://
oreilly.com.
Preface | xi
How to Contact Us
Please address comments and questions concerning this book to the publisher:
O’Reilly Media, Inc.
1005 Gravenstein Highway North
Sebastopol, CA 95472
800-998-9938 (in the United States or Canada)
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707-829-0104 (fax)
We have a web page for this book, where we list errata, examples, and any additional
information. You can access this page at https://oreil.ly/graph-algorithms.
To comment or ask technical questions about this book, send email to bookques‐
tions@oreilly.com.
For news and more information about our books and courses, see our website at
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Acknowledgments
We’ve thoroughly enjoyed putting together the material for this book and thank all
those who assisted. We’d especially like to thank Michael Hunger for his guidance, Jim
Webber for his invaluable edits, and Tomaz Bratanic for his keen research. Finally, we
greatly appreciate Yelp permitting us to use its rich dataset for powerful examples.
xii | Preface
Foreword
What do the following things all have in common: marketing attribution analysis,
anti-money laundering (AML) analysis, customer journey modeling, safety incident
causal factor analysis, literature-based discovery, fraud network detection, internet
search node analysis, map application creation, disease cluster analysis, and analyzing
the performance of a William Shakespeare play. As you might have guessed, what
these all have in common is the use of graphs, proving that Shakespeare was right
when he declared, “All the world’s a graph!”
Okay, the Bard of Avon did not actually write graph in that sentence, he wrote stage.
However, notice that the examples listed above all involve entities and the relation‐
ships between them, including both direct and indirect (transitive) relationships.
Entities are the nodes in the graph—these can be people, events, objects, concepts, or
places. The relationships between the nodes are the edges in the graph. Therefore,
isn’t the very essence of a Shakespearean play the active portrayal of entities (the
nodes) and their relationships (the edges)? Consequently, maybe Shakespeare could
have written graph in his famous declaration.
What makes graph algorithms and graph databases so interesting and powerful isn’t
the simple relationship between two entities, with A being related to B. After all, the
standard relational model of databases instantiated these types of relationships in its
foundation decades ago, in the entity relationship diagram (ERD). What makes
graphs so remarkably important are directional relationships and transitive relation‐
ships. In directional relationships, A may cause B, but not the opposite. In transitive
relationships, A can be directly related to B and B can be directly related to C, while A
is not directly related to C, so that consequently A is transitively related to C.
With these transitivity relationships—particularly when they are numerous and
diverse, with many possible relationship/network patterns and degrees of separation
between the entities—the graph model uncovers relationships between entities that
otherwise may seem disconnected or unrelated, and are undetected by a relational
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