## What are Graphs in the first place?

A mathematical graph, or graph for short, is a structure representing pairwise relationships between objects. A graph is made up of nodes (sometimes called vertices, or points) which are connected by edges (sometimes called arcs, or lines). For example, nodes can embody people, maschines or individual steps in a process. Edges can illustrate the relations between nodes. They can can describe blood relations between people, data exchange between machines or give the interdependence of various steps in a chain of processes. The combination of nodes and the edges between them forms the graph. In practical applications the term network is often used instead of graphs.

Once an application or a problem is transformed to the graph model, powerful concepts, algorithms and analysis techniques from Graph Theory and Network Science immediately apply. For this reason and their wide applicability, graphs and technologies based on graphs have become key elements of many important applications today. Some well-known applications include advertising in social networks, transportation networks or data management applications.

The following example shows how interpreting data as a graph can help us make better sense of structured data. Clearly, the better we understand the complex data we work with the easier it will be to build applications on top of it. In this case, we look at a simple communication network, i.e. people sending emails to each other. However, it is important to emphasize that virtually everything can be seen as a graph.

Finding the best way to model data as a graph and make maximum use of it in an application is a challenging yet important problem.

## Graphs are useful structure

Data capturing the exchange of emails between people can be directly represented as the graph seen here in blue.

We have 10 unique persons forming the set of nodes. For each pair of people that exchanged emails with each other an edge is drawn between their respective nodes. The sum of these edges constitutes the set of edges. Nodes and edges together form a graph, in this case a communication network.

Due to the graph representation interesting information is directly available: The best connected communicator in the graph is Alston with 5 neighbors. Coley and Langdon stick to themselves while Algie has no contacts at all.

While this is a small and simple network, it is not difficult to see how this type of graph thinking applies to large complex networks like Facebook or LinkedIn. It is the graph model that enables the efficient extraction and use of information.

## Nodes are abstract objects

Here the node set is highlighted in red. Additional information is embedded in this graph drawing: The size of a node reflects the total number of mails exchanged with its direct neighbors. If you hover over individual nodes, the total number of mails is given.

In this example nodes represent people. However, in general nodes are abstract objects and can represent any entity. Multiple classes of nodes commonly appear in one graph.

In prominent graphs nodes represent websites, devices, products, customers, messages, events, locations and the list goes on.

## Edges are abstract relations

Here the edge set is highlighted in red. Additional information is embedded in this graph drawing: The thickness of an edge reflects the number of mails exchanged between the two nodes it connects. If you hover over individual edges, the number of mails is given.

In this example edges represent email exchange. However, in general edges are abstract objects and can represent any type of relation. Multiple classes of edges are commonly present in the same graphs.

Edges may also express a directed relation, e.g. Merlin sends 3 mails to Alston. In this example, note that we only talk about mutually exchanged emails ignoring the direction, thus drawing undirected edges suffices.

In prominent graphs edges represent weblinks, connections, buying decisions, selling decisions, subscriptions, time-ordering, streets and the list goes on.

## ... but what makes graphs so useful?

### Graphs are flexible data-tools

Data is most useful if it has meaningful structure. Graphs are ideal to represent and utilize complex connected data.

### Graphs are clean and intuitive

Representing complex connected data as a graph makes it easier to understand. A good visualisation of a graph is worth more than a thousand words.

### Graph technologies have arrived

Whether you need a graph library or an entire distributed graph database to get the job done. Graph tools are available and here to stay.

## Consider using graphs if ...

### ... you write code handling structured data of any kind!

Simply model your use cases as graphs and exploit the power of graph libraries or graph databases to efficiently transform, store and access your structured data. The natural flexibility of the graph model makes it easy to adapt to changing application requirements. This flexibility is responsible for the many forms graph applications take in practice. Examples include: The provisioning of connected Information in social networks like LinkedIn or Facebook, the implementation of complex systems consisting of interconnected sensors or simply the organization of connected data whose complex structure makes using it in tabular form inefficient.

### ... you write code analyzing structured data of any kind!

Representing complex data as a graph opens up powerful analysis and visualizationalization possibilities. It simply is intuitive and fun to explore data that is given as a graph. Try for yourself, zoom in and interact with the complicated-looking graph next to this text. What is this data about? Hint: Nodes are players and edges illustrated the “who with whom”. Applications of graphs in data science and visualization tasks appear organically when the connection between data points become more important that the points themselves. Examples for this include the analysis of social networks or the visualization of complex processes of various sorts.

### ... you don't write code but structured data is still important to your success!

Your operation uses structured data aiming to get the maximum use out of it. However, proper data management requires strategies to meet various challenges connected to the handling of data. Decision makers and visionaries are challenged to understand and keep track of the bigger picture. Thinking in terms of graphs and deploying graph concepts offer additional tools to keep up with the complexity of such challenges.

## You want to know more about graphs? Check out our free online courses!

Proper usage of graphs is not magic. Like any other subject one seeks to start with, proper learning material is the key to get started the right way. We have put our knowledge and experience on the topic to work for you and prepared a set of free introductory online courses to make sure you learn what you need to know fast.

## Our Free Courses.

Our short beginner courses familiarize you with the basic concepts and purpose of graphs. They teach you how to visualize structured data in terms of graphs and introduce you to useful graph tools. In the end you will be in a position to judge for yourself whether you or your organization can benefit by using graphs.

### Introduction to Graphs

Free

Learn the basics of graphs and why you should care

• Concepts
• Applications
• Tools
• Impact

## You plan on taking the next step in using graphs! Excellent, how can we help?

k33 offers a range of services supporting anyone who wants to get started or already works with graphs in a professional capacity. We pride ourselves on being independent experts on almost all things graphs with a supplementary background in Software Engineering, Data Science and Data Engineering. We adhere to the highest standards of work which we successfully implement in both research as well as in an industrial settings. Once you get to know us, you will see that we are different.

## Our Services.

Through the eyes of Data Scientists, Data Engineers and Software Engineers, we add knowledge and skills in the area of graphs to your cause.

### Strategy Session

• Free
• Professional assessment of your situation
• Recommendation for further steps
• Get to know us
• ...

### Keynotes

• Get to know graph technologies
• Understand demand and usage of graphs
• Gauge implications of graph technologies
• ...

### Consultations

• Development of solution concepts based on graphs
• Estimation of required ressources
• Prevention of costly mistakes
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### Workshops

• Effective start into working with graphs
• Realistic case studies
• Promote independet working with graphs
• Application of best practice
• ...

## A thank you to our clients and partners!

Wherever things become complex and connected thinking is required, challenges will be found. Together we combine your domain knowledge with our expertise. In doing so we create new approaches or improve upon time-tested solutions. We are grateful to our clients for their trust.

Michael’s attention to detail and understanding of the client objectives really helped the team steer towards productive cooperation.

#### Dr. Ben Flood

Senior Manager , KPMG Germany

We were working together on a research project that required an interdisciplinary approach from computer science, biology, electrical engineering, and physics. Michael was crucial for the success of this project: His skills combine creative out-of-the-box thinking and thoroughly thought through solutions with a self-organized and timely work schedule that I could completely rely on. I can only highly recommend him!

#### Dr. Matthias Függer

Senior Researcher , CNRS Paris

For more than half a year I had the pleasure to collaborate with Michael in the course of a very work-intensive project. He significantly contributed to the success of by supporting us with his technical expertise. I am happy to recommend Michael without reservation and would be happy to team up again for further future projects.

#### Paul Schwingenschloegl, MSc.

Senior Consultant, PwC GmbH WPG

For almost a year I collaborated with Michael on several projects. I quickly learned to appreciate his opinion and expert statements. They were always clear, precise, well-founded and unbiased with regards to wishful thinking. Open development and expert discussions always yielded a better understanding of the problem at hand and frequently lead to actionable solution strategies. In addition to that, given the fact that Michael and I have different special knowledge, I was able to learn a lot from him. On top of central ideas he frequently showed me best-practice approaches.

#### Dr. rer. nat. Karsten Schwarz

Senior Data Scientist, Lighthouse KPMG Germany

I collaborated with Michael in the course of a project focused on analyzing the flow of people in an urban region. Possible changes between different modes of transport (driving and walking) posed a central challenge to the project. Michael contributed crucially to the development of solution concepts based on Graph Theory. In addition to his technical expertise I quickly learned to appreciate his deliberate and carful way of working and his unreserved willingness to help.

#### Daniel Schulz, M.A.

Senior Associate Consultant, KPMG Deutschland

It is a good idea to have Michael on your team. And it is a better idea to have him on your team in the early stages of your project. The questions he asked did help me understand the problems I wanted to solve. In a sense, Michael brings some very valuable Anti-Scrum to projects. He wants to find the definition of a problem, and then a good solution. While working on a project involving Graphs, and an ETL-pipeline for GIS data, I have learned A LOT, both conceptual and technical. I still use the lessons learned today on other projects. My employer should definitely be happy about the added value that Michael planted in our company, and I am, too, because working with him has been motivating and fun.

#### Dr. Andreas Christ

Senior Data Scientist, Lighthouse KPMG Deutschland

I had the great pleasure of working with Michael on an innovative project in the insurance domain. We were looking into an opportunity to help life insurers accelerate modernization of their IT platforms using statistical algorithms in the data migration processes. Michael did a great job structuring the problem and nailing down the key success factors for our ideas to work. We are currently testing the solution with a couple of major players in Germany. To whomever this concerns – go and grab what Michaels has to offer: creativity, commitment and great teaming. My big recommendation!

#### Mag. Bartek Maciaga

Consulting Partner, KPMG Germany

I met Dr. Michael Dirnberger in a project with focus on optimization. Practical methods were applied to the area of insurance applications, however, the selected methods have a wide range of useful applications in other domains as well. Michael’s scientific expertise and personal strengths soon began to shine in various ways. Examples are the selection of mathematical solution-strategies, the planning of technical implementations as well as his interaction with other team members with whom Michael practices a critical, straight-forward, constructive and goal-oriented approach to the problem at hand. Without reservation, I thus recommend Michael’s engagement in all mentioned areas and beyond!

#### Mag. Frank Wittemann

Senior Manager, KPMG Germany

As a young scientist Dr. Dirnberger made his mark in network analysis and the design of algorithms. He realized early that graphs not only make complex issues understandable but that technologies powerd by graphs can be used to increase the efficiency of various practical applications. With his innovative ideas he is going to unlock the potential of a range of businesses.

#### Prof. Dr. Martin Grube

Professor for Plant Sciences, Karl Franzens University of Graz