The following definitions are taken from:

Gross, Jonathan L., and Jay Yellen. Handbook of Graph Theory<=
/span>. New York: CRC, 2004

unless otherwise noted.

=20- =20
**Weakly Connected**=20- =20
- A directed graph is said to be
*weakly connected*if its underlying undirected graph is*connected*.

**=20**- A directed graph is said to be
**Connected**=20- =20
- An undirected graph is said to be
"= if there exists a walk between every pair of its vertices."*connected*=20

=20
- An undirected graph is said to be
**Mutually Reachable**=20- =20
- "Let
*u*and*v*be vertices in a digraph*G*. The= n*u*and*v*are said to be*mutually reachable**in**G*if*G*contains both a directed*u -**v*walk and a directed*v*-*u*walk. Every vert= ex is regarded as reachable from itself (by the trivial walk)."

*=20*- "Let
**Strongly Connected**=20- =20
- "A digraph is
if every two= vertices are*strongly connected*.*mutually reachable*=20

=20
- "A digraph is
**Strong Component**=20**"A**is a subdigraph induced on a maximal= set ofof a digraph*strong component**G*i= s a maximal strongly connected subgraph of*G*. Equivalently, a*strong component*vertices.*mutually reachable*=20

**=20**=20
**Component**=20- =20
- "The subgraphs of
*G*which are maximal with respect to the prop= erty of beingare called the components= of*connected**G*." =20

=20
- "The subgraphs of
**Graph Density**=20- =20
- "The density of a graph is the ratio of the number of edges and the num= ber of possible edges." (from igraph libra= ry documentation). =20

=20