Matrices and Graphs

The present article is designed to be a contribution to the chapter `Combinatorial Matrix Theory and Graphs' of the Handbook of Linear Algebra, to be published by CRC Press. The format of the handbook is to give just definitions, theorems, and examples; no proofs. In the five sections given below, we present the most im- portant notions and facts about matrices related to (undirected) graphs. 1. Graphs. 2. The adjacency matrix and its eigenvalues. 3. Other matrix representations. 4. Graph parameters. 5. Association schemes.