Ch 9. Graphs
Learning Objectives
By the end of this chapter, students should be able to:
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Interpret and construct graphs using vertices and edges, distinguishing between directed and undirected relationships.
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Identify complete and connected graphs and explain their key properties.
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Analyze directed graphs using indegree and outdegree to evaluate flow and relationships.
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Apply graph theory concepts to information technology problems, including routing, workflows, and data structures.
In the digital world, relationships between entities (users, devices, or data points) are often best represented using graphs and graph theory provides a framework for modelling and analyzing these relationships, making it an essential tool in IT. This chapter introduces three foundational types of graphs. Complete graphs are ideal for modelling fully connected networks and peer-to-peer systems. Connected graphs are crucial for ensuring communication or data flow in systems. Directed graphs (digraphs) allow us to model one-way relationships such as hyperlinks, dependencies, or control flows. Through visual diagrams, mathematical definitions, and practical examples, you’ll learn how to interpret and construct graphs that represent complex systems.
