There is a class of computational problems that can be best represented in terms of graphs. Such problems can be solved using a class of algorithms called graph algorithms. For example, graph algorithms can be used to efficiently search a value in a graphical representation of data. To work efficiently, these algorithms will first need to discover the structure of the graph. They also need to find the right strategy for following the edges of the graph to read the data stored in the vertices. As graph algorithms need to search values in order to work, efficient searching strategies lie at the center of designing efficient graph algorithms. Using graph algorithms is one of the most efficient ways of searching for information in complex, interconnected data structures that are linked through meaningful relationships. In today's era of big data, social media, and distributed data, such techniques are becoming increasingly important and useful.

In this chapter, we will start by presenting the basic concepts behind graph algorithms. Then, we will present the basics of network analysis theory. Next, we will look at the various techniques that can be used to traverse graphs. Finally, we will look at a case study showing how graph algorithms can be used for fraud detection.

In this chapter, we will go through the following concepts:

• Different ways of representing graphs
• Introducing network theory analysis
• Understanding graph traversals
• Case study: fraud analytics 
• Techniques for establishing a neighborhood in our problem space

By the end of this chapter, you will have a good understanding of what graphs are and how to work with them to represent interconnected data structures and mine information from entities that are related by direct or indirect relationships, as well as use them to solve some complex real-world problems.