A *simple graph* is a pair *(V,E)* where *V*
is set (of *nodes*) and *E* is a set of
*2*-elementary subsets of *V*, which are called
*edges*. General graphs are allowed to have multiple edges
between a pair of nodes or *loops*, that is, edges from a
node to itself.

The simple graphs are precisely the *1*-dimensional
abstract simplicial complexes.

A *directed* graph (also called *digraph*) has arcs
instead of edges, where an *arc* is an ordered pair of
nodes.

Typically, our graphs are finite.

- Norman Biggs:
*Algebraic Graph Theory*, 2nd ed. Cambridge Mathematical Library. Cambridge University Press (1994). - Bela Bollobas:
*Modern Graph Theory*, Graduate Texts in Mathematics**184**. New York, Springer (1998). - Douglas B. West:
*Introduction to Graph Theory*, Upper Saddle River, NJ: Prentice Hall (1996).