Sets-Nodes-Edges: Representing Complex Networks in Graph Theory
Networked systems, such as the internet, can be large and enormously complex. This poses a challenge to scientists and engineers who study such networks. Powerful mathematical concepts, such as graph theory, can be used to effectively analyze complex networks.Copyright The Opte Project http://commons.wikimedia.org/wiki/File:Internet_map_1024.jpg
Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.
Complex networks of interacting components are at the core of many problems of scientific and engineering interest, and this realization has caused the interdisciplinary study of networks to grow rapidly during the past decade. Neural engineers represent the connectivity of neurons in the human brain using graphs, whereas, electrical engineers use graphs to understand large and complex systems, such as the internet. The software engineers at Facebook use graphs to enable us to visualize social relationships, whereas, bioengineers study how an infectious disease, like the flu, might spread over a social network. Understanding the mathematics behind graph theory can help biomedical engineers and scientists to develop better cancer treatments and electrical engineers to design faster and more reliable communication networks among electronic devices.
After this lesson, students should be able to:
- Provide examples of complex networks and formally represent them by graphs.
- Draw a visual representation of a graph and provide a formal description in terms of nodes and edges.
- Identify the degree of a node in a graph and calculate the degree distribution of the graph.