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
![Graphviz, changing the size of edge](https://cdn-ak-scissors.b.st-hatena.com/image/square/98d6f053a97a87156775f60757c60865d0f2c47d/height=288;version=1;width=512/https%3A%2F%2Fcdn.sstatic.net%2FSites%2Fstackoverflow%2FImg%2Fapple-touch-icon%402.png%3Fv%3D73d79a89bded)