Key-words: matrix, graph, digraph. The way of relating matrices and graphs or digraphs is well known. Many properties of matrices are re ected in characteristics of their associated graphs (digraphs), and, conversely, to certain types of graphs correspond matrices with peculiar properties. The objective of this dissertation is to collect, systematize, and present some results already known about relationships be- tween graphs (digraphs) and matrices. Basic connections between graphs (digraphs) and matrices are presented along the rst chapters. In the fol- lowing chapters, concrete situations where properties of matries are deduced from the charateristics of their associated graphs (digraphs), and vice-versa, are presented. In this scope, properties of matrices related with chordal graphs, CDUM and cyclic digraphs are explored and, nally, properties of graphs associated to Fiedler matrices are studied.