# EECI09: Graph theory

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This lecture gives an introduction to some concepts and tools in graph theory. After giving the basic definitions of graphs and properties of graphs, we introduce the Laplacian of a matrix and discuss its properties and uses. Special emphasis is placed on the eigenvalues of the Laplacian, including the bounding of those eigenvalues using the Gershgorin disk theorem. The consensus problem is introduced as an example of the use of the basic concepts.

## Lecture Materials

- Lecture slides: An Introduction to Graph Theory

## Further Reading

Algebraic Graph Theory G. Royle and C. Godsil, Springer, Graduate Texts in Mathematices, 2001.

Consensus problems in networks of agents with switching topology and time-delays, R. Olfati-Saber and R. M. Murray, IEEE Transactions on Automatic Control, vol. 49, 1520-1533, Sept. 2004. A good reference for continuous time consensus algorithms.

Coordination of groups of mobile autonomous agents using nearest neighbor rules, A. Jadbabaie, J. Lin, and A. S. Morse, IEEE Transactions on Automatic Control, Vol. 48, No. 6, June 2003, pp. 988-1001. A good reference for discrete time consensus algorithms and theoretical explanation for consensus of multi-agent systems using nearest neighbor rules.