Mastering Algorithms with C

Chapter 11. Graphs

Graphs are some of the most flexible data structures in computing. In fact, most other data structures can be represented as graphs, although representing them in this way is usually more complicated. Generally, graphs are used to model problems defined in terms of relationships or connections between objects. Objects in a graph may be tangible entities such as nodes in a network or islands in a river, but they need not be. Often objects are less concrete, such as states in a system or transactions in a database. The same is true for connections and relationships among the objects. Nodes in a network are physically connected, but the connections between states in a system may simply indicate a decision made to get from one state to the next. Whatever the case, graphs model many useful and interesting computational problems.

This chapter covers:

Graphs

Flexible data structures typically used to model problems defined in terms of relationships or connections between objects. Objects are represented by vertices , and the relationships or connections between the objects are represented by edges between the vertices.

Search methods

Techniques for visiting the vertices of a graph in a specific order. Generally, either breadth-first or depth-first searches are used. Many graph algorithms are based on these basic methods of systematically exploring a graph’s vertices.

Some applications of graphs are:

Graph algorithms

Algorithms that solve problems modeled by graphs (see ...