I wanted to supplement shuvalov's answer. penwidth is indeed the correct command. Additionally, in shuvalov's answer penwidth is both a node and an edge property--also correct.
The distinction i wanted to make:
penwidth, when used as a node
property (e.g., "NodeA" [penwidth =
5]) affects the border line weight
for that node
penwidth, when used as a edge
property affects the line weight of
the edge (default value is "1",
specifying penwidth=2 will make the
edge appear in bold type
if you want to change the line weight
of an edge, you do not need to change
penwidth for the two nodes
connected by that edge (as shuvalev's
answer might suggest)
for a directed graph (the edges have
a direction) you might also wish to change the
size/weight of the arrowhead and
arrowtail, along with the edge
weight, so that all three remain
proportional
the length of an edge can be changed
by setting the weight property, as
elsewhere, the default value is 1.0;
increasing that value increases the
cost of stretching this edge during
rendering (i.e., the drawing
algorithm applies a higher penalty to
solutions in which this edge is
longer); notice that the edge from 1
to 4 is shorter than the edge from 1
to 2.
The following code should illustrate all of this. The rendered graph is shown below the code.